Strongly nonlinear periodic parabolic equation in Orlicz spaces
DOI:
https://doi.org/10.24193/subbmath.2025.1.04Keywords:
The periodic solution, Nonlinear parabolic equation, Galerkin method, Orlicz spaces, weak solutions,Abstract
In this paper, we prove the existence of a weak solution to the following nonlinear periodic parabolic equations in Orlicz-spaces:
∂u/∂t− div(a(x,t,∇u)) = f(x, t)
where −div(a(x, t,∇u)) is a Leray-Lions operator defined on a subset of \(W^{1,x}_{0} L_{M}(Q)\). The Δ2-condition is not assumed and the data f belongs to \(W{−1,x}E_{\overline{M}}(Q)\). The Galerkin method and the fixed point argument are employed in the proof.
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