6 papers
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 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…