No. 5 (264), issue 11Pages 43 - 53

The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity

M.O. Korpusov
In this paper we continue our consideration of equations with gradient nonlinearities. In this paper, we consider initial-boundary value problem in a bounded domain with smooth boundary for non-local in time equation with gradient nonlinearity and prove the local solvability of the strong generalized sense, in addition, we obtain sufficient conditions for the destruction of a finite time and sufficient conditions for global in time solubility.
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Keywords
nonlocal equation with gradient nonlinearity, Sobolev type equations, the destruction of the solutions.
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