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The Cauchy problem for the fast Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour
Matteo Bonforte, Nikita Simonov, Diana Stan
We study fine global properties of nonnegative solutions to the Cauchy Problem for the fast -Laplacian evolution equation on the whole Euclidean space, in the so-cal…
Discrete Carleman estimates and three balls inequalities
Aingeru Fernández-Bertolin, Luz Roncal, Angkana Rüland +1
We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the un…
Porous medium equation with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation , which describes a flow thr…
Finite and infinite speed of propagation for porous medium equations with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We study a porous medium equation with fractional potential pressure: for , and .…
The Fisher-KPP equation with nonlinear fractional diffusion
Diana Stan, Juan Luis Vázquez
We study the propagation properties of nonnegative and bounded solutions of the class of reaction-diffusion equations with nonlinear fractional diffusion: $u_{t} + (-Δ)^s (u^m)=f(u…