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

Isamu Fukuda, Hitoshi Ishii, Masayoshi Tsutsumi

Research output: Contribution to journalArticle

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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Superharmonic Function
Harmonic functions
Uniqueness of Solutions
Generalized Solution
Viscosity Solutions
Weak Solution
Cauchy Problem
Uniqueness
Equivalence
Viscosity
Class

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Uniqueness of solutions to the cauchy problem for ut - uΔu + γ|∇u|2 = 0. / Fukuda, Isamu; Ishii, Hitoshi; Tsutsumi, Masayoshi.

In: Differential and Integral Equations, Vol. 6, No. 6, 1993, p. 1231-1252.

Research output: Contribution to journalArticle

Fukuda, I, Ishii, H & Tsutsumi, M 1993, 'Uniqueness of solutions to the cauchy problem for ut - uΔu + γ|∇u|2 = 0', Differential and Integral Equations, vol. 6, no. 6, pp. 1231-1252.
Fukuda, Isamu ; Ishii, Hitoshi ; Tsutsumi, Masayoshi. / Uniqueness of solutions to the cauchy problem for ut - uΔu + γ|∇u|2 = 0. In: Differential and Integral Equations. 1993 ; Vol. 6, No. 6. pp. 1231-1252.
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