Affiliation:
1. Université Sidi Mohammed Ben Abdellah , Ecole Nationale des sciences Appliques . Fés . Morocco
2. Université Sidi Mohammed Ben Abdellah , Département de Mathématiques, Laboratoire LAMA. Faculté des Sciences Dhar-Mahrez , B.P 1796 Atlas Fés . Morocco
Abstract
Abstract
We prove existence of entropy solutions to general class of unilateral nonlinear parabolic equation in inhomogeneous Musielak-Orlicz spaces avoiding ceorcivity restrictions on the second lower order term. Namely, we consider
{
u
≥
ψ
in
Q
T
,
∂
b
(
x
,
u
)
∂
t
-
d
i
v
(
a
(
x
,
t
,
u
,
∇
u
)
)
=
f
+
d
i
v
(
g
(
x
,
t
,
u
)
)
∈
L
1
(
Q
T
)
.
$$\left\{ \matrix{ \matrix{ {u \ge \psi } \hfill & {{\rm{in}}} \hfill & {{Q_T},} \hfill \cr } \hfill \cr {{\partial b(x,u)} \over {\partial t}} - div\left( {a\left( {x,t,u,\nabla u} \right)} \right) = f + div\left( {g\left( {x,t,u} \right)} \right) \in {L^1}\left( {{Q_T}} \right). \hfill \cr} \right.$$
The growths of the monotone vector field a(x, t, u, ᐁu) and the non-coercive vector field g(x, t, u) are controlled by a generalized nonhomogeneous N- function M (see (3.3)-(3.6)). The approach does not require any particular type of growth of M (neither Δ2 nor ᐁ2). The proof is based on penalization method.
Subject
Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis
Reference18 articles.
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