Compactly supported solution of the time-fractional porous medium equation on the half-line

Łukasz Płociniczak; Mateusz Świtała

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arXiv · 1803.03016

Compactly supported solution of the time-fractional porous medium equation on the half-line

Łukasz Płociniczak·Mateusz Świtała

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Abstract

In this work we prove that the time-fractional porous medium equation on the half-line with Dirichlet boundary condition has a unique compactly supported solution. The approach we make is based on a transformation of the fractional integro-differential equation into a nonlinear Volterra integral equation. Then, the shooting method is applied in order to facilitate the analysis of the free-boundary problem. We further show that there exists an exactly one choice of initial conditions for which the solution has a zero which guarantees the no-flux condition. Then, our previous considerations imply the unique solution of the original problem.

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Łukasz Płociniczak, Mateusz Świtała. 2018-03-08. Compactly supported solution of the time-fractional porous medium equation on the half-line. https://arxiv.org/abs/1803.03016

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