Uniqueness of solutions to the cauchy problem for ut - uΔu + γ|∇u|2 = 0

Isamu Fukuda, Hitoshi Ishii, Masayoshi Tsutsumi

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11 Citations (Scopus)

Abstract

We prove the uniqueness of weak solutions and of viscosity solutions of the Cauchy problem for ut -uΔu+γ|∇ u|2 = 0 in RN × (0, T) in the class of semi-super harmonic functions. We also discuss the equivalence of these two notions of generalized solutions.

Original languageEnglish
Pages (from-to)1231-1252
Number of pages22
JournalDifferential and Integral Equations
Volume6
Issue number6
Publication statusPublished - 1993
Externally publishedYes

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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