187 citations · 206 across the 7 of their papers we have counts for
14 papers
On the elasto-plastic filtration equation
Arturo de Pablo, Fernando Quiros, Julio D. Rossi
We study the fully nonlinear heat equation posed in a bounded domain with Dirichlet boundary conditions. Here if , if $s>0…
Travelling-wave behaviour in doubly nonlinear reaction-diffusion equations
Yihong Du, Alejandro Garriz, Fernando Quiros
We study a family of reaction-diffusion equations that present a doubly nonlinear character given by a combination of the -Laplacian and the porous medium operators. We consider…
A heat equation with memory: large-time behavior
Carmen Cortazar, Fernando Quiros, Noemi Wolanski
We study the large-time behavior in all norms and in different space-time scales of solutions to a heat equation with a Caputo -time derivative posed in . Th…
Interior second derivative estimates for nonlinear diffusions
Gregoire Loeper, Fernando Quiros
By an extension of of some estimates due to Crandall and Pierre and Di Benedetto we derive consequences for fully nonlinear parabolic equations of the form $\dt v + F(t,x,D^2v)=0$,…
Logarithmic corrections in Fisher-KPP type Porous Medium Equations
Yihong Du, Fernando Quiros, Maolin Zhou
We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in $L^\in…
Regularity theory for singular nonlocal diffusion equations
Arturo de Pablo, Fernando Quirós, Ana Rodríguez
We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be sin…
Near field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case
Carmen Cortázar, Fernando Quirós, Noemí Wolanski
We consider the porous medium equation in an exterior two-dimensional domain which excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in [Gi…
Near field asymptotic behavior for the porous medium equation on the half-line
Carmen Cortázar, Fernando Quirós, Noemí Wolanski
Kamin and Vázquez proved in 1991 that solutions to the Cauchy-Dirichlet problem for the porous medium equation on the half line with zero boundary data and nonnega…
A HELE-SHAW problem for tumor growth
Antoine Mellet, Benoît Perthame, Fernando Quiros
We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limi…
Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
Carmen Cortázar, Manuel Elgueta, Fernando Quirós +1
We study the long time behavior of solutions to the nonlocal diffusion equation in an exterior one-dimensional domain, with zero Dirichlet data on the compleme…
Asymptotic Behavior for a nonlocal diffusion equation on the half line
Carmen Cortazar, Manuel Elgueta, Fernando Quiros +1
We study the large time behavior of solutions to a non-local diffusion equation, with smooth, radially symmetric and compactly supported, posed in wi…
The Hele-Shaw asymptotics for mechanical models of tumor growth
Benoît Perthame, Fernando Quirós, Juan Luis Vázquez
Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones con…
Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
C. Cortazar, M. Elgueta, F. Quiros +1
The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, , in an exterior domain, , which excludes one or several holes, and w…
A fractional porous medium equation
Arturo de Pablo, Fernando Quiros, Ana Rodriguez +1
We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, in $…