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 - <p style="text-align: justify;">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 $f$ &nbsp;belongs to $L^{1}(Q_T)$. The proof of an existence solution is based on the penalization methods.</p>