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

Goro Akagi, Stefano Melchionna

研究成果: Article査読

抄録

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.

本文言語English
論文番号10
ジャーナルNonlinear Differential Equations and Applications
26
2
DOI
出版ステータスPublished - 2019 4 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

フィンガープリント 「Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル