Weak solutions of parabolic equations in non-cylindrical domains

Russell M. Brown, Wei Hu, Gary M. Lieberman

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

In their classical work, Ladyzhenskaya and Ural'tseva gave a definition of weak solution for parabolic equations in cylindrical domains. Their definition was broad enough to guarantee the solvability of all such problems but narrow enough to guarantee the uniqueness of these solutions. We give here some alternative definitions which are appropriate to non-cylindrical domains, and we prove the unique solvability of such problems.

Original languageEnglish
Pages (from-to)1785-1792
Number of pages8
JournalProceedings of the American Mathematical Society
Volume125
Issue number6
DOIs
StatePublished - 1997

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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