This article is cited in 13 papers

On the Blow-Up of the Solution of an Equation Related to the Hamilton–Jacobi Equation

M. O. Korpusov

M. V. Lomonosov Moscow State University

Abstract: A new model three-dimensional third-order equation of Hamilton–Jacobi type is derived. For this equation, the initial boundary-value problem in a bounded domain with smooth boundary is studied and local solvability in the strong generalized sense is proved; in addition, sufficient conditions for the blow-up in finite time and sufficient conditions for global (in time) solvability are obtained.

Keywords: third-order equation of Hamilton–Jacobi type, blow-up of solutions, electric potential in a crystalline semiconductor, Dirichlet problem, Galerkin approximation, Browder–Minty theorem, Lipschitz-continuous operator.

UDC: 517.957

Received: 26.03.2012
Revised: 08.06.2012

DOI: 10.4213/mzm8955

 English version: Mathematical Notes, 2013, 93:1, 90–101

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