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Parabolic equations in Orlicz spaces. (English) Zbl 1108.35082

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.

MSC:

35K55 Nonlinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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