25 citations · 54 across the 8 of their papers we have counts for
15 papers
Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions
Carmen Cortázar, Fernando Quirós, Noemí Wolanski
We study the decay/growth rates in all norms of solutions to an inhomogeneous nonlocal heat equation in involving a Caputo -time derivative and a power …
Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions
Carmen Cortázar, Fernando Quirós, Noemí Wolanski
We study the decay/growth rates in all norms of solutions to an inhomogeneous nonlocal heat equation in involving a Caputo -time derivative and a power …
Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes
Arturo de Pablo, Fernando Quirós, Antonella Ritorto
We prove the existence of an extremal function in the Hardy-Littlewood-Sobolev inequality for the energy associated to an stable operator. To this aim we obtain a concentration-com…
Large-time behavior for a fully nonlocal heat equation
Carmen Cortázar, Fernando Quirós, Noemí Wolanski
We study the large-time behavior in all norms and in different space-time scales of solutions to a nonlocal heat equation in involving a Caputo -time deriva…
Coupling local and nonlocal evolution equations
Alejandro Gárriz, Fernando Quirós, Julio D. Rossi
We prove existence, uniqueness and several qualitative properties for evolution equations that combine local and nonlocal diffusion operators acting in different subdomains and cou…
Late Central Engine Activity in GRB 180205A
R. L. Becerra, A. M. Watson, N. Fraija +16
We present optical photometry of the afterglow of the long GRB 180205A with the COATLI telescope from 217 seconds to about 5 days after the {\itshape Swift}/BAT trigger. We analyse…
Anisotropic nonlocal diffusion equations with singular forcing
Arturo de Pablo, Fernando Quirós, Ana Rodríguez
We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-han…
A free boundary problem of Stefan type with nonlocal diffusion
Carmen Cortázar, Fernando Quirós, Noemí Wolanski
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportiona…
Nonlocal filtration equations with rough kernels
Arturo de Pablo, Fernando Quirós, Ana Rodríguez
We study the nonlinear and nonlocal Cauchy problem \[ \partial_{t}u+\mathcal{L}φ(u)=0 \quad\text{in }\mathbb{R}^{N}\times\mathbb{R}_+,\qquad u(\cdot,0)=u_0, \] where …
Asymptotic behavior for a nonlocal diffusion equation in exterior domains: the critical two-dimensional case
Carmen Cortázar, Manuel Elgueta, Fernando Quirós +1
We study the long time behavior of bounded, integrable solutions to a nonlocal diffusion equation, , where is a smooth, radially symmetric kernel with supp…
Derivation of a Hele-Shaw type system from a cell model with active motion
Benoît Perthame, Fernando Quirós, Min Tang +1
We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the n…
Classical solutions and higher regularity for nonlinear fractional diffusion equations
Juan Luis Vázquez, Arturo de Pablo, Fernando Quirós +1
We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion posed for , , wi…
Classical solutions for a logarithmic fractional diffusion equation
Arturo de Pablo, Fernando Quirós, Ana Rodríguez +1
We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion posed…
A nonlocal one-phase Stefan problem that develops mushy regions
Cristina Brändle, Emmanuel Chasseigne, Fernando Quirós
We study a nonlocal version of the one-phase Stefan problem which develops mushy regions, even if they were not present initially, a model which can be of interest at the mesoscopi…
A general fractional porous medium equation
Arturo de Pablo, Fernando Quirós, Ana Rodríguez +1
We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \{ll} \dfrac{\partial u}{\partial t} + (-Δ)^{σ/2} (|u|^{m-1}u…