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Volume 33, Issue 1
Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems via a Sequence of Penalized Equations

A. Aberqi, J. Bennouna & H. Redwane

Anal. Theory Appl., 33 (2017), pp. 29-45.

Published online: 2017-01

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  • 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.

  • AMS Subject Headings

47A15, 46A32, 47D20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-33-29, author = {}, title = {Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems via a Sequence of Penalized Equations}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {1}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n1.4}, url = {http://global-sci.org/intro/article_detail/ata/4614.html} }
TY - JOUR T1 - Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems via a Sequence of Penalized Equations JO - Analysis in Theory and Applications VL - 1 SP - 29 EP - 45 PY - 2017 DA - 2017/01 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n1.4 UR - https://global-sci.org/intro/article_detail/ata/4614.html KW - Obstacle parabolic problems, entropy solutions, penalization methods. AB -

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.

A. Aberqi, J. Bennouna & H. Redwane. (1970). Entropy Unilateral Solution for Some Noncoercive Nonlinear Parabolic Problems via a Sequence of Penalized Equations. Analysis in Theory and Applications. 33 (1). 29-45. doi:10.4208/ata.2017.v33.n1.4
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