Arturo de Pablo

most citedClassical solutions for a logarithmic fractional diffusion equation

6 citations · 6 across the 2 of their papers we have counts for

collaborators

3 papers

math.AP2024

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…

math.AP2018

Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions

Raul Ferreira, Arturo de Pablo

We study the behaviour of nonnegative solutions to the quasilinear heat equation with a reaction localized in a ball $u_{t} = Δ u^{m} + a (x) u^{p},$ for $m > 0$ , $0 < p \leq max {1, m}$ , $a(x)=\…

math.AP2012★ 6 cited

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 $\partial_{t} u + (- Δ)^{1/2} lo g (1 + u) = 0,$ posed…