Research on Partial differential equations

Recently we have established well posedness results for kinetic models of Fokker-Planck type describing angionenesis processes and developed convergent numerical schemes. Previously, we studied long time asymptotics for Vlasov-Poisson-Fokker-Planck and Vlasov-Poisson-Boltzmann problems arising in plasma and semiconductor physics, combining classical constructions of fundamental solutions with modern compactness results for kinetic operators. Using Hardy spaces, we developed a L1 theory for incompressible Navier-Stokes equations, and explored the behavior of solutions of vorticity equations with measure data. Earlier, we studied energy decay in nonlinear wave problems with damping terms.

Analysis of a two phase flow model of biofilm spread, A. Carpio, G. Duro, Nonlinear Analysis 224, 113538, 2024 [pdf] [arxiv]

Well posedness of fluid-solid mixture models for biofilm spread, A. Carpio, G. Duro, Applied Mathematical Modelling 124, 64-85, 2023 [pdf] [arxiv]

Positivity preserving high order schemes for kinetic models of angiogenesis, A. Carpio, E. Cebrián, International Journal on Nonlinear Sciences and Numerical Simulation 23(6), 917-929, 2022 [pdf] [arxiv]

Incorporating cellular stochasticity in solid-fluid mixture biofilm models, A. Carpio, E. Cebrián, Entropy 22(2), 188, 2020 [pdf]

A convergent numerical scheme for integrodifferential kinetic models of angiogenesis, L.L. Bonilla, A. Carpio, M. Carretero, G. Duro, M. Negreanu, F. Terragni, Journal of Computational Physics 375, 1270-1294, 2018 [pdf]

Constructing solutions for a kinetic model of angiogenesis in annular domains, A. Carpio, G. Duro, M. Negreanu, Applied Mathematical Modelling 45, 303-322, 2017 [pdf] [arxiv]

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis, A. Carpio, G. Duro, Nonlinear Analysis-Real World Applications 30, 184-212, 2016 [pdf] [arxiv] [Audioslides]

Well posedness of an angiogenesis related integrodifferential diffusion model, A. Carpio, G. Duro, Applied Mathematical Modelling 40 (9-10), 5560-5575, 2016 [pdf] [arxiv]

Long time asymptotics for the semiconductor Vlasov-Poisson-Boltzmann equations, A. Carpio, E. Cebrian, F.J. Mustieles, Mathematical Models and Methods in Applied Sciences 11(9), 1631-1665, 2001 [pdf] [archivo]

Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals, A. Carpio, SJ Chapman, JJL Velazquez, SIAM Journal on Applied Mathematics 61(6), 2168-2199, 2001 [pdf] [arxiv]

Numerical study of hyperbolic equations with integral constraints arising in semiconductor theory, A. Carpio, P. Hernando, M. Kindelan, SIAM Journal on Numerical Analysis 39(1), 168-191, 2001 [pdf] [arxiv]

Asymptotic profiles for convection-diffusion equations with variable diffusion, A. Carpio, G Duro, Nonlinear Analysis- Theory, Methods and Applications 45(4), 407-433, 2001 [pdf] [archivo]

Long-time behavior for solutions of the Vlasov-Poisson-Fokker-Planck equation, A. Carpio, Mathematical Methods in the Applied Sciences 21(11), 985-1014, 1998 [pdf] [archivo]

Large time behavior in convection-diffusion equations, A. Carpio, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze (Ser IV), 23(3), 551-574, 1996 [pdf] [archivo]

Large-time behavior in incompressible Navier-Stokes equations, A. Carpio, SIAM Journal on Mathematical Analysis 27 (2), 449-475, 1996 [pdf] [archivo]

Large time behavior in incompressible Navier-Stokes equations, A. Carpio, Zeitschrift für angewandte Mathematik und Mechanik (ZAMM) 76 (S2), 495-496, 1996

Asymptotic-behavior for the vorticity equations in dimensions two and three, A. Carpio, Communications in Partial Differential Equations 19(5-6), 827-872, 1994 [pdf] [archivo]

Existence of global solutions to some nonlinear dissipative equations, A. Carpio, Journal de Mathématiques Pures et Appliquées 73(5), 471-488, 1994 [archivo]

Unicité et comportement asymptotique pour des équations de convection diffusion scalaires, A. Carpio, Comptes Rendus de l'Académie des Sciences. Série I. Mathématique (CRAS Paris), 319, Ser I, 51-56, 1994

Comportement asymptotique dans les équations de Navier-Stokes, A. Carpio, CRAS Paris, 319, Ser I, 223-228, 1994

Comportement asymptotique des solutions des équations du tourbillon en dimensions 2 et 3, A. Carpio, CRAS Paris, 316, Ser I, 1289-1294, 1993

Existence de solutions globales rétrogrades pour des équations des ondes non linéaires dissipatives, A. Carpio, CRAS Paris, 316, Ser I, 803-808, 1993

Sharp estimates of the energy for the solutions of some dissipative second order evolution problems, A. Carpio, Potential Analysis 1(3), 265-289, 1992 [pdf] [archivo]

A nonexistence result for a nonlinear equation involving critical Sobolev exponent, AC Rodriguez, M. Comte, R. Lewandowski, Annales de l'Institut Henri Poincaré-Analyse Non Linéaire 9(3), 243-261, 1992 [pdf] [archivo]