FPM 2006, vol. 12, no. 4, pp. 3-19

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 3-19

Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity

S. N. Antontsev
S. I. Shmarev

Abstract

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We prove the existence and uniqueness of weak solutions of the Dirichlet problem for the nonlinear degenerate parabolic equations

u

_t = div (a|u|^g(x,t) Ñu) + b|u|^g(x,t)/2Ñu - c|u|^s(x,t)
-
2u + d, where

a

c

, and

d

are given functions of the arguments

x

t

, and

u(x,t)

, and the exponents of nonlinearity

g(x,t) and

s(x,t) are known measurable and bounded functions of their arguments.

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Last modified: February 17, 2007