Existence result for nonlinear parabolic problems with $L^1$-data
Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 483-508
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We study the existence of solutions of the nonlinear parabolic problem$$\displaylines{
\frac{\partial u}{\partial t}-\mathop{ \rm div}[|Du-{\mit\Theta}(u)|^{p-2}(Du-
{\mit\Theta}(u))] +\alpha(u)=f
\quad\ \hbox{in } \mathopen{]}0, T\mathclose{[}\times{\mit\Omega},\cr
(|Du-{\mit\Theta}(u)|^{p-2}(Du-{\mit\Theta}(u)))\cdot \eta + \gamma(u)=g \quad\
\hbox{on } \mathopen{]}0, T\mathclose{[}\times\partial{\mit\Omega}, \cr
u(0,\cdot )=u_0 \quad\ \hbox{in } {\mit\Omega},\cr}
$$
with initial data in $L^1$. We use a time
discretization of the continuous problem by the Euler forward scheme.
Keywords:
study existence solutions nonlinear parabolic problem displaylines frac partial partial mathop div du mit theta p du mit theta alpha quad hbox mathopen mathclose times mit omega du mit theta p du mit theta cdot eta gamma quad hbox mathopen mathclose times partial mit omega cdot quad hbox mit omega initial time discretization continuous problem euler forward scheme
Affiliations des auteurs :
Abderrahmane El Hachimi 1 ; Jaouad Igbida 2 ; Ahmed Jamea 1
@article{10_4064_am37_4_6,
author = {Abderrahmane El Hachimi and Jaouad Igbida and Ahmed Jamea},
title = {Existence result for nonlinear parabolic problems with $L^1$-data},
journal = {Applicationes Mathematicae},
pages = {483--508},
year = {2010},
volume = {37},
number = {4},
doi = {10.4064/am37-4-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am37-4-6/}
}
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%0 Journal Article %A Abderrahmane El Hachimi %A Jaouad Igbida %A Ahmed Jamea %T Existence result for nonlinear parabolic problems with $L^1$-data %J Applicationes Mathematicae %D 2010 %P 483-508 %V 37 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4064/am37-4-6/ %R 10.4064/am37-4-6 %G en %F 10_4064_am37_4_6
Abderrahmane El Hachimi; Jaouad Igbida; Ahmed Jamea. Existence result for nonlinear parabolic problems with $L^1$-data. Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 483-508. doi: 10.4064/am37-4-6
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