Applied sciences are a source of challenging models defined in terms of partial differential equations. Conservation laws for mixtures are ubiquitous in tissue and biofilm studies. We are developing well posedness theories for mixture models set in moving domains. Kinetic models of Fokker-Planck type often arise when deriving continuum macroscopic limits from stochastic microscopic description. We have established well posedness results for Fokker-Planck type equations arising in angionenesis studies 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] |
