Elmahi, A.; Meskine, D. Parabolic equations in Orlicz spaces. (English) Zbl 1108.35082 J. Lond. Math. Soc., II. Ser. 72, No. 2, 410-428 (2005). The authors deal with the following problem: \[ u_t+A(u)=f(x,t), \quad (x,t)\in\Omega\times(0,T), \]\[ u(x,t)=0, \quad (x,t)\in \partial\Omega\times(0,T), \]\[ u(x,0)=u_0(x), \quad x\in\Omega, \] where \(A(u)=-{\text{div}}(a(x,t,u,\nabla u))+a_0(x,t,u,\nabla u)\) and \(\Omega\) is a bounded open set in \({\mathbb R}^n\). The existence of solutions for this problem in the Orlicz-Sobolev spaces is shown. Reviewer: Hanna Marcinkowska (Wrocław) Cited in 42 Documents MSC: 35K55 Nonlinear parabolic equations 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:parabolic initial-boundary value problem; Orlicz-Sobolev spaces; the existence of solutions PDFBibTeX XMLCite \textit{A. Elmahi} and \textit{D. Meskine}, J. Lond. Math. Soc., II. Ser. 72, No. 2, 410--428 (2005; Zbl 1108.35082) Full Text: DOI