FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2006, VOLUME 12, NUMBER 4, PAGES 319
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 (au^{g(x,t)}
Ñu) +
bu^{g(x,t)/2}Ñu

cu^{s(x,t)

2}u + d,
where $a$, $$b,
$c$,
and $d$ are
given functions of the arguments $x$, $t$, and $u(x,t)$, and the exponents
of nonlinearity $$g(x,t) and $$s(x,t)
are known measurable and bounded functions
of their arguments.
Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06401h.htm
Last modified: February 17, 2007