Browsing by Subject "nonlinear parabolic problems"
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Item type:Article, Access status: Open Access , Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions(Wydawnictwa AGH, 2023) Bahja, Hamid ElWe study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard $p(x,t),q(x,t)$-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time $L^{\infty}$ bounds for the weak solutions.