Geodesic
On the Blow-Up of the Solution of an Equation Related to the Hamilton--Jacobi Equation
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 81-95.

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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. 
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M. O. Korpusov. On the Blow-Up of the Solution of an Equation Related to the Hamilton--Jacobi Equation. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a7/

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