Geodesic
The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 43-53

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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.
Keywords: nonlocal equation with gradient nonlinearity, the destruction of the solutions.
Mots-clés : Sobolev type equations 
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     author = {M. O. Korpusov},
     title = {The {Destruction} of the {Solution} of the {Nonlocal} {Equation} with {Gradient} {Nonlinearity}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {43--53},
     publisher = {mathdoc},
     number = {11},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2012_11_a4/}
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M. O. Korpusov. The Destruction of the Solution of the Nonlocal Equation with Gradient Nonlinearity. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 43-53. http://geodesic.mathdoc.fr/item/VYURU_2012_11_a4/