Ma, T. F.; Soriano, J. A. On weak solutions for an evolution equation with exponential nonlinearities. (English) Zbl 0940.35033 Nonlinear Anal., Theory Methods Appl. 37, No. 8, A, 1029-1038 (1999). 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 \(g(s)s\geq 0.\) Reviewer: Marie Kopáčková (Praha) Cited in 27 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs Keywords:quasilinear evolution equation; Galerkin approximations; Dirichlet boundary conditions; Orlicz spaces × Cite Format Result Cite Review PDF Full Text: DOI