Study of some anisotropic parabolic problems with degenerate coercivity
Abstract
The main aim of this paper is the studying of the anisotropic parabolic problems described by
\frac{\partial u}{\partial t}-\sum_{i=1}^{N} D^{i}a_{i}(x,t,u, \nabla u)=f(x,t,u) in Q_{T}=\Omega\times(0,T),
u=0 on\Sigma_{T}=\partial\Omega\times (0,T),
u(x,0)=u_{0}(x) in \Omega,
where \Omega is a bounded open subset of \mathbb{R^{N}} with N\geq 2. We addressed the existence of renormalized solutions result for (\ref{abs}). We point out that the function f(x,t,u) satisfies only some growth conditions with respect to u, and the initial data u_{0} belongs to L^{1}(\Omega).
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DOI: https://doi.org/10.52846/ami.v53i1.2001