25 citations · 34 across the 7 of their papers we have counts for
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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…
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 …
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 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…