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

Isamu Fukuda; Hitoshi Ishii; Masayoshi Tsutsumi

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

Isamu Fukuda, Hitoshi Ishii, Masayoshi Tsutsumi

Research output: Contribution to journal › Article

Abstract

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

Original language	English
Pages (from-to)	1231-1252
Number of pages	22
Journal	Differential and Integral Equations
Volume	6
Issue number	6
Publication status	Published - 1993
Externally published	Yes

Fingerprint

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

Fukuda, I., Ishii, H., & Tsutsumi, M. (1993). Uniqueness of solutions to the cauchy problem for u_t - uΔu + γ|∇u|² = 0. Differential and Integral Equations, 6(6), 1231-1252.

@article{107a76a435844913a100ea4de51c576e,

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

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.",

author = "Isamu Fukuda and Hitoshi Ishii and Masayoshi Tsutsumi",

year = "1993",

language = "English",

volume = "6",

pages = "1231--1252",

journal = "Differential and Integral Equations",

issn = "0893-4983",

publisher = "Khayyam Publishing, Inc.",

number = "6",

}

TY - JOUR

T1 - Uniqueness of solutions to the cauchy problem for ut - uΔu + γ|∇u|2 = 0

AU - Fukuda, Isamu

AU - Ishii, Hitoshi

AU - Tsutsumi, Masayoshi

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972529832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972529832&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972529832

VL - 6

SP - 1231

EP - 1252

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 6