Papers in international journals 2017-18

Caroccia M., Cheeger $N$-clusters, Calc. Var. Partial Differential Equations, Vol.56 (2017), no.2, Art. 30.

Cristian Barbarosie, Daniel Tortorelli, Seth Watts, On domain symmetry and its use in homogenization, Computer Methods in Applied Mechanics and Engineering, Vol.320 (2017), pp.1-45.

A. C. Barroso, J. Matias, M. Morandotti and D.R. Owen, Second-order structured deformations: relaxation, integral representation, Arch. Rat. Mech. Anal., Vol.225, n.3 (2017), pp.1025-1072.

A. C. Barroso, J. Matias, M. Morandotti and D.R. Owen, Explicit formulas for relaxed disarrangement densities arising from structured deformations, Mathematics and Mechanics of Complex Systems, Vol. 5 (2017), n. 2, pp.163-189.

M. Baía, A. C. Barroso and J. Matias, A model for phase transitions with competing terms, Quarterly Journal of Mathematics, Vol.68 (2017) n.3, pp.957-1000.

A.C.Barroso, J. Matias and P.M.Santos, Differential Inclusions and A-quasiconvexity, Mediterranean Journal of Mathematics Vol.14 (2017), n.3, Art.116, 14pp.

Simão Correia and Mario Figueira, Existence and stability of spatial plane waves for the Incompressible Navier-Stokes in R^3, Journal of Mathematical Fluid Mechanics, published online in 2017, pp.1-9.

Simão Correia and Mario Figueira, Spatial plane waves for the nonlinear Schrodinger equation: Local existence and stability results, Communications in Partial Differential Equations (2017), Vol. 42, n.4, pp.519-555.

Pedro Antunes, Cristian Barbarosie and Anca-Maria Toader, Detection of holes in an elastic body based on eigenvalues and traces of eigenmodes, Journal of Computational Physics, Vol.333 (2017), pp.352-368.

L. Saraiva. A introdução na China dos Elementos de Euclides , Actas do Encontro Leituras Portuguesas da China dos séculos XVI a XVII, Mafra, Centro de Estudos Geográficos da Universidade de Lisboa/Palácio Nacional de Mafra, Europress (2017), pp. 111-129. 

C.O.R. Sarrico, Multiplication of distributions and travelling wave solutions for the Keyfitz-Kranzer system, Taiwanese Journal of Mathematics (2018).

C.O.R. Sarrico, A. Paiva, Delta Shock Waves in the Shallow Water System, Journal of Dynamics and Differential Equations (2017), pp.1–12

C.O.R. Sarrico, A. Paiva, The Multiplication of Distributions in the Study of a Riemann Problem in Fluid Dynamics, Journal of Nonlinear Mathematical Physics, Vol.24 (2017), n.3, pp.328–345.

C.O.R. Sarrico, A. Paiva, New distributional travelling waves for the nonlinear Klein-Gordon equation, Differential and Integral Equations, Vol.30 (2017), n.11–12, pp. 853–878.

N. Soave, H. Tavares, S. Terracini, A. Zilio, Variational problems with long-range interaction, Arch Rational Mech Anal (2017), pp.1–30.

A. Pistoia, H. Tavares, Spiked solutions for Schrödinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions, Journal of Fixed Point Theory and Applications, Vol.19 (2017), n.1, pp 407–446.

Hugo B. da Veiga, On the extension to slip boundary conditions of a Bae and Choe regularity criterionfor the Navier-Stokes equations. The half-space case, J. Math. Anal. Appl., Vol.453 (2017), pp. 212–220.

N. Van Goethem, Incompatibility-governed singularities in linear elasticity with dislocations, Math. Mech. Solids, Vol. 22 (2017), n.8, pp. 1688-1695.

S. Amstutz and N. Van Goethem, Incompatibility-governed elasto-plasticity for continua with dislocations, Proc. R. Soc. Lond., published online in 2017.

M. Xavier, N. Van Goethem, A.A. Novotny, J.M.C. Farias,  E.A. Fancello, Topological Derivative-Based Fracture Modelling in Brittle Materials: A Phenomenological Approach,  Engineering Fracture Mechanics , Vol.179 (2017), pp. 13-27.

N. Van Goethem, Incompatibility-governed singularities in linear elasticity with dislocations, Math. Mech. Solids, Vol.22, no.8, pp.1688-1695.

N. Van Goethem, Front migration for the dislocation strain in single crystals, Comm. Math, Sc., Vol15 (2017), n.7, pp. 1688-1695.

J.P.Dias, F.Oliveira, On a quasilinear non-local Benney system, Hyperbolic Diff. Eq., Vol.14 (2017), n.1, pp.135-156.

H.B. de Oliveira and A. Paiva, Existence for a one-equation turbulent model with strong nonlinearities, J. Elliptic Parabol. Equ., Vol.3 (2017), n.1-2, pp. 65-91.

H.B. de Oliveira and A. Paiva, A stationary one-equation turbulent model with applications in porous media, J. Math. Fluid Mech, published online in 2017, pp.1–25

J. Ferreira and H.B. de Oliveira, Parabolic reaction-diffusion systems with nonlocal coupled diffusivity terms, Discrete Contin. Dyn. Syst. - A, Vol.37 (2017), n.5, pp.2431-2453.

M. Negri, R. Scala, A quasi-static evolution generated by local energyminimizers for an elastic material with a cohesive interface, NonlinearAnal. Real World Appl., Vol.38 (2017), pp. 271-305.

E. Bonetti, E. Rocca, R. Scala, G. Schimperna, On the strongly dampewave equation with constraint, Communications in Partial Differential Equations, Vol.42 (2017), n.7, pp.1042-1064.

R. Scala, A weak formulation for a rate-independent delamination evolu-tion with inertial and viscosity effects subjected to unilateral constraint, Interfaces Free Bound., Vol.19 (2017). n.1, pp. 79-107.

R. Scala, N. Van Goethem, Analytic and geometric properties of dislo-cation singularities, accepted on Proc. Roy. Soc. Edinburgh Sect. A. (2017).

R. Scala, G. Schimperna, A contact problem for viscoelastic bodies with
inertial effects and unilateral boundary constraints
, European J. of Appl.
Math, Vol.28 (2017), no.1, pp. 91-122.

E. Rocca, R. Scala, The sharp interface limit for diffuse interface modelsrelated to tumor growth, J. Nonlinear Sci., Vol.27 (2017). n.3.

Antontsev  S.N., Shmarev S.I., The energy method. Application to PDEs of hydrodynamics with nonstandard growth, J. Phys: Conf.Ser. 894 (2017). 

Antontsev, S. , Almeida, R. M. P.,  Duque, J., Discrete solutions for the porous medium equation with  absorption and variable exponents, Mathematics and Computers in Simulation,  Vol.137 (2017), pp. 109-129.

Antontsev S,  Kh. Khompysh,  Kelvin-Voight equation with p-Laplacian and damping term: Existence, uniqueness and  blow- up . Mathematical Analysis  and Applications, Vol.446 (2017), pp.1255-1273.

Antontsev, S. , Almeida, R. M. P.,  Duque, J.  Discrete solutions for the porous medium equation with  absorption and variable exponents, Mathematics and Computers in Simulation, Vol.137 (2017), pp.109-129.

Antontsev S,  Kh. KhompyshKelvin-Voight equation with p-Laplacian and damping term: Existence, uniqueness and  blow- up, Mathematical Analysis  and Applications, Vol.446 (2017),  pp.1255-1273.

Antontsev, S. N. and Khompysh, Kh, Generalized  Kelvin--Voigt equations with p-Laplacian and  source/absorption terms, Journal of Mathematical Analysis and Applications,  Vol. 456 (2017), n.1, pp.99-116.

Antontsev S.N and  Kuznetsov I.V., Existence of entropy measure-valued solutions of forward-backward $p$-parabolic equations,  Siberian Electronic Mathematical  Reports,  Vol.14 (2017), pp. 774-93.

Antontsev, Stanislav N., Almeida, Rui M. P.; Duque, José C. M., On the finite element method for a nonlocal degenerate parabolic problem, Comput. Math. Appl., Vol.73 (2017), no.8, pp.1724–1740.

.  Antontsev S., Shmarev S.,  Higher regularity of solutions of singular equations with variable nonlinearity, Applicable Analysis (2017), pp.1-22.

Book Chapters 2017

Anca-Maria Toader and Cristian Barbarosie, Optimization of Eigenvalues and Eigenmodes by using the Adjoint Method, Topological Optimization and Optimal Transport in the Applied Sciences, Radon Series on Computational and Applied Mathematics, 17, 2017-08.

Papers in international journals 2016

A. C. Barroso, J. Matias, M. Morandotti e D. R. Owen, Explicit formulas for relaxed disarrangement densities arising from structured deformations, to appear in Mathematics and Mechanics of Complex Systems

P. Antunes, C. Barbarosie, A.M. Toader, Detection of holes in an elastic body based on eigenvalues and traces of eigenmodes, to appear in J. Comp. Phys. DOI: 10.1016/

N. Van Goethem, The Frank tensor as a boundary condition in intrinsic linearized elasticity, J. Geom. Mech., 8(4), (2016).

N. Van Goethem,  Dislocation-induced linear-elastic strain dynamics by a Cahn–Hilliard-type equation, Mathematics and Mechanics of Complex Systems 4-2, (2016), 169--195.

R. Scala, N. Van Goethem. Constraint reaction and the Peach–Koehler force for dislocation networks. Mathematics and Mechanics of Complex Systems 4-2 (2016), 105--138.

N. Van Goethem,  Direct expression of Incompatibility in curvilinear systems, The ANZIAM J.,  58, (2016), 33–50.

R. Scala, N. Van Goethem, Currents and dislocations and the continuum scale, Meth. Appl. Analysis, 23 (2016), 1-34.

S. Amstutz and N. Van Goethem, Analysis of the incompatibility operator and application in intrinsic elasticity with dislocations, Siam J. Math. Analysis, 48 (2016), 320-348.

J.P. Dias, M. Figueira and V. V. Konotop, Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup, Studies in Appl.Mathem. 136 (2016), 241-262.

J.P. Dias, M. Figueira and F. Oliveira, Existence and linearized stability of solitary waves for a quasilinear Benney system, Proc.Royal Soc.Edinburgh, Section A, 146 (2016), 547-564.

J.P. Dias, M. Figueira and V. V. Konotop, The Cauchy problem for coupled nonlinear Schrödinger equations with linear damping: Local and global existence and blowup of solutions, Chin. Ann. Math. B, 37 (2016), 665-682.

S. Correia, Characterization of ground-states for a system of M coupled semilinear Schrödinger equations and applications,  Journal of Differential Equations, 260 (2016),3302-3326.

S. Antontsev, J.I. Diaz, Finite speed of propagation and waiting time for local solutions of degenerate equations in viscoelastic media or heat flows with memory, J. Elliptic and Parabolic Equations (JEPE), Vol. 2, 2016, p. 201-210.

S.N. Antontsev, I.V. Kuznetsov, Singular Perturbations of forward-backward p-parabolic equations, J. Elliptic and Parabolic Equations (JEPE), Vol. 2, 2016, p. 357-370.

S. Antontsev, S. Shmarev, On the localization of solutions of doubly nonlinear parabolic equations with nonstandard growth in filtration theory, Applicable Analysis, 95 (2016), no.10, pp.2162-2180.

R.M.P. Almeida, S.N. Antontsev and J.C.M.Duque, On a nonlocal degenerate parabolic problem, Nonlinear analysis: Real World Applications 27(2016), 146-157.

S. Antontsev, S. Shmarev, J. Simsen and M.S. Simsen, On the evolution p-Laplacian with nonlocal memory. Nonlinear Anal. 134 (2016), 31–54.

R.M.P. Almeida, S.N. Antontsev , J.C.M. Duque and J.A. Ferreira, A reaction–diffusion model for the non-local coupled system: existence, uniqueness, long-time behaviour and localization properties of solutions, IMA J. Appl. Math., 81 (2016), 344-364.

S.N. Antontsev , F. Miranda  and  L. Santos, Blow-up and finite time extinction for p(x,t)-curl systems arising in electromagnetism, Journal  Math. Anal. Appl., 440 (2016), .300-322.

J.C.M. Duque, S.N.Antontsev, R.M.P. Almeida and J. Ferreira, The Euler–Galerkin finite element method for a nonlocal coupled system of reaction–diffusion type, J. Comp. Appl. Math., 296 (2016),116-126.

S.N. Antontsev and H.B. de Oliveira, Evolution problems of Navier–Stokes type with anisotropic diffusion, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. (online 2015).

S. Antontsev, S. Shmarev, On a class of fully nonlinear parabolic equations. Adv. Nonlinear Anal, 2016.

Paulo Rocha, Frank Raischel, João P. Boto, Pedro G. Lind, Uncovering the evolution of nonstationary stochastic variables: The example of asset volume-price fluctuations, Phys. Rev. E 93 (2016)

Book Chapters

Anca-Maria Toader and Cristian Barbarosie, Optimization of Eigenvalues and Eigenmodes by using the Adjoint Method, in Topological Optimization and Optimal Transport In the Applied Sciences, Radon Series on Computational and Applied Mathematics vol. 17, by Maitine Bergounioux (Editor), Édouard Oudet (Editor), Martin Rumpf (Editor), Guilaume Carlier (Editor), Thierry Champion (Editor). Walter De Gruyter Inc (October 10, 2016) ISBN-13: 978-3110439267

Papers in international journals and book 2015

Research papers:

G. Maggiani, R. Scala, N. Van Goethem, A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity, Math. Meth. Appl. Sc.,38 (2015), 5217-5230.

N. Van Goethem, Cauchy elasticity with dislocations in the small strain assumption, Appl. Math.Lett., 96 (2015), 94-99.

V.V.Shelukin and N.V. Chemetov, Global solvability of the one-dimensional Cosserat-Bingham fluid equations,  J. Math..Fluid Mech.,17 (2015), 495-511.

S. Correia, Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the L2 –critical case, Commun. Contemp. Math.17 (2015) 1450030 [16 pages]

Cazenave, S. Correia, F. Dickstein, F.B. Weissler, A Fujita-type blowup result and low energy scattering for a nonlinear Schrödinger equation, São Paulo Journal of Mathematical Sciences, 9 (2015), 146-161.

H.B. de Oliveira, Anisotropically diffused and damped Navier-Stokes equationsDiscrete Contin. Dyn. Syst, 2015 Suppl., (2015), 349-358.

J.C.M. Duque, S.N. Antontsev and R.M.P Almeida,  Application of the moving mesh method to the porous medium equation with variable exponent, Math. Comp. Simul.,118 (2015),177-185.

S. N. Antontsev and S. Shmarev, On the Cauchy problem for evolution p(x)-Laplace equation, Port. Math.,72 (2015),125-144.

S. Antontsev and S. Shmarev ,  On the localization of solutions of doubly nonlinear parabolic equations with nonstandard growth in filtration theory, Applicable Analysis (online 2015).

J.F. Rodrigues. On the mathematical analysis of thick fluids. J. Math. Sci. (N.Y.), 210 (2015), 835–848.

J.F.Rodrigues and L. Santos,  Solutions for linear conservation laws with gradient constraint. Port. Math., 72 (2015), 161–192.

C.O.R. Sarrico, The Riemann problem for the Brio system: a solution containing a Dirac mass obtained via a distributional product. Russ. J. Math. Phys., 22 (2015), 518–527.


C.O.R. Sarrico and A.Paiva, Products of distributions and collision of a δ-wave with a δ-wave in a turbulent model. J. Nonlinear Math. Physics, 22 (2015), 381-394.

Paulo Rocha, Frank Raischel, João Pedro Boto, Pedro G. Lind, Optimal models of extreme volume-prices are time-dependent, Journal of Physics: Conference Series 574 (2015)


L.M.R.Saraiva, Étienne Bézout in Portugal: the reform of the Portuguese University and beyond (1772–1838). Historia Math. 42 (2015), 14–46.

Biographical paper:

H. Beirão da Veiga and J.F. Rodrigues.To the jubilee of João Paulo de Carvalho Dias on the occasion of his seventieth anniversary, Port. Math., 72 (2015), 81–82.


Antontsev S.N., Shmarev S.I., Evolution PDEs with nonstandard growth conditions. Existence, Uniqueness, Localization, Blow-up. Series: Atlantis Studies in Differential Equations, Vol. 4, 2015, XIV, 393 p. 1 illus. ISBN 978-94-6239-111-6.


Artigos em revistas internacionais 2013-14


P. Amorim and J.P.Dias. A nonlinear model describing a short wave-long wave
interaction in a viscoelastic medium, Quart. Appl. Math., 71(2013),417-132.

P.Amorim, J.P.Dias, M.Figueira and Ph. LeFloch. The linear stability of shock waves for the Nonlinear Schrodinger-Inviscid Burgers system, J. Dyn. Diff. Eq., 25 (2013), 49-69.

P.Amorim and M.Figueira. Convergence of a numerical  scheme for a coupled Schrodinger – KdV system, Rev. Mat. Complut., 26 (2013), 409-426.

P.Amorim and M.Figueira. Convergence  of a finite difference method for the KdV and modified KdV equations with L2 data, Port. Math., 70 (2013), 23-50.  5155&vol=70&iss=1&rank=3.

S.Antontsev and P.Amorim, Young measure solutions for wave equation with p(x,t)-Laplacian: Existence and blow up, Nonlinear Analysis: Theory, Methods and Applications, 92(2013), 153-167.

S.Antontsev and J. Ferreira, Existence, uniqueness and blow up for hyperbolic equations with nonstandard growth conditions, Nonlinear Analysis : Theory, Methods & Applications, 93(2013), 62-77.

A. J. Corcho, F. Oliveira and J.D. Silva, Local and global well posedness for the critical Schrödinger-Debye system, Proc.Amer.Math.Soc.,141(2013),3485-3499.

J.P.Dias and M.Figueira. On the blowup of solutions of a Schrodinger equation with an inhomogeneous damping coefficient, Comm. Contemp. Math.,16(2014),1350036-1350046.

S.Antontsev, J.P.Dias and M.Figueira. Complex Ginzburg-Landau equation with absorption: existence, uniqueness and localization properties.J. Math. Fluid, Mechanics,16(2014), 211-223.

T.Cazenave, J.P.Dias and M.Figueira. Finite-time blow-up for a complex   Ginzburg-Landau equation with linear driving. J. Evolution Eq.,14 (2014), 403-415.

J.P.Dias, M.Figueira, V. Konotop and D. Zezyulin. Supercritical blowup in coupled parity-time-symmetric nonlinear Schrodinger equation, Studies in Appl. Math.,133 (2014), 422-440.

C.O.R. Sarrico. New distributional global solutions for the Hunter- Saxton equation, Abstr.Appl.Anal. (2014), Art. ID 809095, 9pp.

C.O.R. Sarrico. A distributional product approach to δ-shock wave  solutions for a generalized pressureless gas dynamics system, Internat. J. Math. 1450007, 25 (2014),12 pp.

C.O.R. Sarrico. The Brio system with initial conditions involving Dirac masses: a result afforded by a distributional product, Chin. Ann. Math Ser.B 35 (2014), 941-954.

S. Antontsev  and J. Ferreira. On a viscoelastic plate equation with strong damping and p(x,t)- Laplacian. Existence and uniqueness. Diff. Integral Equations, 27 (2014), 1147-1170.

H. B. Oliveira, Existence of weak solutions for the generalized Navier-Stokes equations with damping, NoDEA Nonlinear Differential Equations Appl. 20 (2013), no. 3, 797–824.

Challal, S.; Lyaghfouri, A.; Rodrigues, J. F.; Teymurazyan, R. On the regularity of the free boundary for quasilinear obstacle problems. Interfaces Free Bound. 16 (2014), no. 3, 359–394.

Rodrigues, José Francisco; Tavares, Hugo Increasing powers in a degenerate parabolic logistic equation. Chin. Ann. Math. Ser. B 34 (2013), no. 2, 277–294.

Antontsev S., H.B. de Oliveira, Analysis of the existence for the steady Navier- Stokes equations with anisotropic diffusion, Advances in Differential Equations, Volume 19, Numbers 5-6 (2014), 441-472.

Antontsev, S. N.; de Oliveira, H. B. Asymptotic behavior of  trembling fluids. Nonlinear Anal. Real World Appl. 19 (2014), 54–66.

Antontsev S.N., Shmarev S, Doubly Degenerate Parabolic Equations with Variable Nonlinearity II: Blow-up and Extinction in a Finite Time, Nonlinear Analysis: Theory, Methods and Applications, 95 (2014), 483-498.

Antontsev, S. N., Duque, J. C. M.; Almeida, R. M. P. Numerical study of the porous medium equation with absorption, variable exponents of nonlinearity and free boundary. Appl. Math. Comput. 235 (2014), 137–147.

Antontsev S., Almeida R. and Duque J., Convergence of the finite element method for the porous media equation with variable exponent, SIAM J. Numer Anal., 51(6), 2013, 3483-3504.

Antontsev S. N., Chipot  M. and  Shmarev S.,  Uniqueness and comparison    theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions, Comm. on Pure and Appl. Anal., Volume 12, (2013), 1527–1546.

C. Barbarosie, A.M. Toader, Optimization of bodies with locally periodic microstructure by varying the periodicity pattern, Networks and Homogeneous Media, 9(3) 2014

M. Baía, A. C. Barroso, M. Chermisi and J. Matias, Coupled second order singular perturbations for phase transitions, Nonlinearity, 26 (2013), 1-41

A. C. Barroso, G. Croce and A. M. Ribeiro, Sufficient conditions for existence of solutions to vectorial differential inclusions and applications, Houston Journal of Mathematics, 39 (2013), 929-967

A.C. Barroso and J. P. Silva, Mutual inductance between piecewise-linear loops, American Journal of Physics, 81 (2013), 829-835

N.V. Chemetov, W. Neves. “The multidimensional Muskat initial boundary value problem”. Interfaces and Free Boundaries, 16, N° 3, (2014) 339-357.

N.V. Chemetov, F. Cipriano. “Inviscid limit for Navier–Stokes equations in domains with permeable boundaries”. Applied Math. Letters. 33 (2014) 6–11.

Castaing, C.; Monteiro Marques, M. D. P.; Raynaud de Fitte, P. Some problems in optimal control governed by the sweeping process. J. Nonlinear Convex Anal. 15 (2014), no. 5, 1043–1070. 2013/2014

S. Amstutz, A. Novotny, N. Van Goethem, Minimal partitions and image classification with a gradient-free perimeter approximation, Inv. Pbl. Imag., 8 (2), 361-387, 2014 (IF:1.388)

S. Amstutz, A. Novotny, N. Van Goethem, Topological sensitivity analysis for elliptic differential operators of order 2m, J. Diff. Eqs., 256 (4), 1735-1770,2014 (IF: 1.570)

N. Van Goethem, Thermodynamical forces in single crystals with dislocations, Z. ang. Math. Phys., 65 (3), 549-586, 2014 (IF:1.214)

N. Van Goethem, Fields of bounded deformation for mesoscopic dislocations, Mathematics and Mechanics of Solids, 19 (5), 579-600, 2014 (IF:0.85)

N.V. Chemetov, F. Cipriano. The inviscid limit for slip boundary conditions. In the book“Hyperbolic Problems: Theory, Numerics, Applications ", AIMS on Applied Mathematics, vol. 8 (2014), 431-438.

L. Arruda, N.V. Chemetov, Embedding theorem for bounded deformations in domains with cusps, Mathematical Methods in the Applied Sciences. Volume 37, Issue 17, 2739–2745  2014

N.V. Chemetov, F. Cipriano, Boundary layer problem: Navier-Stokes equations and Euler equations, Nonlinear Analysis: Real World Applications, 14, N° 6 (2013), 2091–2104.

N.V. Chemetov, F. Cipriano, The Inviscid Limit for the Navier–Stokes Equations with Slip Condition on Permeable Walls, Journal of Nonlinear Science, 23, N° 5 (2013), 731-750. URL:

N.V. Chemetov, W. Neves, The generalized Buckley-Leverett System: Solvability, Archive for Rational Mechanics and Analysis, 208, N° 1 (2013), 1-24.