Title

Global Solvability for the Porous Medium Equation with Boundary Flux Governed by Nonlinear Memory

Document Type

Article

Publication Date

3-2015

Publication Source

Journal of Mathematical Analysis and Applications

Volume

423

Issue

2

Inclusive pages

1183-1202

DOI

10.1016/j.jmaa.2014.10.041

Peer Reviewed

yes

Abstract

We introduce the study of global existence and blow up in finite time for nonlinear diffusion equations with flux at the boundary governed by memory. Via a simple transformation, the memory term arises out of a corresponding model introduced in previous studies of tumor-induced angiogenesis. The present study is also in the spirit of extending work on models of the heat equation with local, nonlocal, and delay nonlinearities present in the boundary flux. Specifically, we establish an identical set of necessary and sufficient conditions for blow up in finite time as previously established in the case of local flux conditions at the boundary.

Keywords

nonlinear diffusion equation, global existence, blow up in finite time, memory boundary condition

Disciplines

Mathematics

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