On backward problem for fractional spherically symmetric diffusion equation with observation data of nonlocal type

Data regularization for a backward time-fractional diffusion problem

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

On the Inverse Problem for a Fractional Diffusion Equation

We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

quenching time for a nonlocal diffusion problem with large initial data

Nonlinear nonlocal diffusion: A fractional porous medium equation

We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion,  ∂u ∂t + (−∆)σ/2(|u|m−1u) = 0, x ∈ RN , t > 0, u(x, 0) = f(x), x ∈ RN , with data f ∈ L1(RN ) and exponents 0 < σ < 2, m > m∗ = (N − σ)+/N . An L1-contraction semigroup is constructed. Nonnegative solutions are proved to be continuous and strictly positive for all x ∈ RN , t > 0...