Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems via a Sequence of Penalized Equations

Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems via a Sequence of Penalized Equations

Year:    2017

Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 29–45

Abstract

We give an existence result of the obstacle parabolic equations $$\frac{\partial b(x,u)}{\partial t} -div(a(x,t,u,\nabla u))+div(\phi(x,t,u)) =f\quad \text{in}\ \ Q_T,$$ where $b(x,u)$ is bounded function of $u$, the term $- {\rm div}(a(x,t,u,\nabla u))$ is a Leray-Lions type operator and the function $\phi$ is a nonlinear lower order and satisfy only the growth condition. The second term $f$  belongs to $L^{1}(Q_T)$. The proof of an existence solution is based on the penalization methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2017.v33.n1.4

Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 29–45

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Obstacle parabolic problems entropy solutions penalization methods.