Ana Carpio, Applied Mathematics - Fluid, kinetic, wave equations
 
We have recently established well posedness results and numerical schemes for kinetic models of Fokker-Planck type describing angionenesis processes: existence, uniqueness of solutions, together with stability bounds in terms of the data. 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.
  • Positivity preserving high order schemes for kinetic models of angiogenesis (with E. Cebrián), International Journal on Nonlinear Sciences and Numerical Simulation, 2021 to appear [pdf] [arxiv]
  • A convergent numerical scheme for integrodifferential kinetic models of angiogenesis (with L.L. Bonilla, 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 (with 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 (with G. Duro), Nonlinear Analysis-Real World Applications 30, 184-212, 2016 [pdf] [arxiv] [Audioslides]

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

  • Long time asymptotics for the semiconductor Vlasov-Poisson-Boltzmann equations (with E. Cebrian, FJ Mustieles), Mathematical Models and Methods in Applied Sciences 11(9), 1631-2199, 2001  [pdf] [archivo]

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

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

  • Asymptotic-behavior in convection-diffusion equations, 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, SIAM Journal on Mathematical Analysis 27 (2), 449-475, 1996 [pdf] [archivo]

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

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

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

  • Unicité et comportement asymptotique pour des équations de convection diffusion scalaires, CRAS Paris, 319, Ser I, 51-56, 1994

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

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

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

  • Sharp estimates of the energy for the solutions of some dissipative second order evolution problems, Potential Analysis 1(3), 165-289, 1992 [pdf] [archivo]

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

last modified: 1-Sept-2021