25 citations · 45 across the 7 of their papers we have counts for
10 papers
Fractional very fast diffusion equations in Lebesgue spaces: uniqueness and smoothing effects
Mohammed-El-Mahdi Boudaoud, Arturo de Pablo, Fernando Quirós
We investigate forward and backward smoothing effects in Lebesgue spaces and for the Cauchy problem associated to the nonlinear and nonlocal fra…
Blow-up for a double nonlocal heat equation
Raúl Ferreira, Arturo de Pablo
We study the blow-up question for the diffusion equation involving a nonlocal derivative in time defined by convolution with a nonnegative and nonincreasing kernel, and a nonlocal…
Positivity and asymptotic behaviour of solutions to a generalized nonlocal fast diffusion equation
Arturo de Pablo, Fernando Quirós, Jorge Ruiz-Cases
We study the positivity and asymptotic behaviour of nonnegative solutions of a general nonlocal fast diffusion equation, \[\partial_t u + \mathcal{L}φ(u) = 0,\] and the interplay b…
Blow-up for a fully fractional heat equation
Raúl Ferreira, Arturo de Pablo
We study the existence and behaviour of blowing-up solutions to the fully fractional heat equation with , where $\mathc…
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 …
Nonlocal heat equations: decay estimates and Nash inequalities
Cristina Brändle, Arturo de Pablo
We obtain -- decay estimates, for solutions of nonlocal heat equations of the form . Here is an integral oper…
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 concave-convex elliptic problem involving the fractional Laplacian
Cristina Brändle, Eduardo Colorado, Arturo de Pablo
We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize complet…
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 $…