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Nonexistence of solution for higher order evolution equations and inequalities. (English) Zbl 1156.35344

Summary: Many authors have established results for existence and nonexistence of nonlinear evolution P.D.Es in the form \(\frac{\partial^ku} {\partial t^k}-\delta_1\Delta u+\delta_2\Delta^2u=f(x,\nabla u,u)\) where \(\delta_1,\delta_2\in\{0,1\}\). In this paper we prove the nonexistence results for the general form that contains this forms for \(f(x,\nabla u,u)=|x|^{-\gamma}|u|^q\) or \(|\nabla u^q|^p\).

MSC:

35G30 Boundary value problems for nonlinear higher-order PDEs
35R45 Partial differential inequalities and systems of partial differential inequalities
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