Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint

Goro Akagi, Stefano Melchionna

Research output: Contribution to journalArticlepeer-review

Abstract

The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage Mechanics, is reformulated as a mixed form of two different types of doubly nonlinear evolution equations. Global (in time) solutions to some approximate problems are constructed by performing a time discretization argument and by taking advantage of energy techniques based on specific structures of the equation. Moreover, a variational comparison principle for (possibly non-unique) approximate solutions is established and it also enables us to obtain a local solution as a limit of approximate ones.

Original languageEnglish
Article number10
JournalNonlinear Differential Equations and Applications
Volume26
Issue number2
DOIs
Publication statusPublished - 2019 Apr 1

Keywords

  • Blow-up in finite time
  • Mixed doubly nonlinear equations
  • Porous medium equation
  • Unidirectional evolution
  • Variational comparison principle

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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