Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations

Chen, Guo Wang. "Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 431-443. <http://eudml.org/doc/247588>.

@article{Chen1994,
abstract = {The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation \[ u\_t=-A(t)u\_\{x^4\}+B(t)u\_\{x^2\}+g(u)\_\{x^2\}+f(u)\_\{x\}+h(u\_\{x\})\_\{x\}+G(u) \] with the initial boundary value conditions \[ u(-\ell ,t)=u(\ell ,t)=0,\quad u\_\{x^2\}(-\ell ,t)=u\_\{x^2\}(\ell ,t)=0,\quad u(x,0)=\varphi (x), \] or with the initial boundary value conditions \[ u\_\{x\}(-\ell ,t)=u\_\{x\}(\ell ,t)=0,\quad u\_\{x^3\}(-\ell ,t)=u\_\{x^3\}(\ell ,t)=0,\quad u(x,0)=\varphi (x), \] are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.},
author = {Chen, Guo Wang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear parabolic equation; initial boundary value problem; classical global solutions; classical global solutions},
language = {eng},
number = {3},
pages = {431-443},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations},
url = {http://eudml.org/doc/247588},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Chen, Guo Wang
TI - Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 431
EP - 443
AB - The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation \[ u_t=-A(t)u_{x^4}+B(t)u_{x^2}+g(u)_{x^2}+f(u)_{x}+h(u_{x})_{x}+G(u) \] with the initial boundary value conditions \[ u(-\ell ,t)=u(\ell ,t)=0,\quad u_{x^2}(-\ell ,t)=u_{x^2}(\ell ,t)=0,\quad u(x,0)=\varphi (x), \] or with the initial boundary value conditions \[ u_{x}(-\ell ,t)=u_{x}(\ell ,t)=0,\quad u_{x^3}(-\ell ,t)=u_{x^3}(\ell ,t)=0,\quad u(x,0)=\varphi (x), \] are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.
LA - eng
KW - nonlinear parabolic equation; initial boundary value problem; classical global solutions; classical global solutions
UR - http://eudml.org/doc/247588
ER -