Parabolic Minkowski convolutions of solutions to parabolic boundary value problems

Kazuhiro Ishige, Paolo Salani

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We introduce a new kind of convolution, which is a sort of parabolic version of the classical supremal convolution of convex analysis. This operation allows us to compare solutions of different parabolic problems in different domains. As examples of applications of our main result, we study the parabolic concavity of solutions to parabolic boundary value problems, analyzing in particular the case of heat equation with an inhomogeneous term and with a nonlinear reaction term. We also apply our technique to the study of the dead core problem obtaining new results about necessary conditions for the existence of a dead core and estimates of the dead core time, proving some optimality of the ball.

Original languageEnglish
Pages (from-to)640-673
Number of pages34
JournalAdvances in Mathematics
Volume287
DOIs
Publication statusPublished - 2016 Jan 10

Keywords

  • Dead core
  • Heat equation
  • Minkowski addition
  • Power concavity

ASJC Scopus subject areas

  • Mathematics(all)

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