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On weak solutions for an evolution equation with exponential nonlinearities. (English) Zbl 0940.35033

Using the Galerkin approximations and some results on the Orlicz spaces the author proves the existence and exponential (for \(n=2\)) or power (for \(n\geq 3\)) decay of a solution to the initial boundary value problem for the equation \( u_{tt}-\sum _{j=1}^n(|\nabla u|^{n-2}u^{x_j})_{x_j}-\triangle u_t+g(u)=f (t>0, x\in \Omega \subset \mathbb{R}^n)\) with Dirichlet boundary conditions, where \(g(u)\) is of an exponential growth and satisfies the condition \(g(s)s\geq 0.\)

MSC:

35B40 Asymptotic behavior of solutions to PDEs
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