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Matematicheskie Zametki, 2013, Volume 93, Issue 1, Pages 81–95
DOI: https://doi.org/10.4213/mzm8955 (Mi mzm8955) 		 
This article is cited in 9 scientific papers (total in 9 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
Full-text PDF (532 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm8955
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.
Received: 26.03.2012
Revised: 08.06.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 1, Pages 90–101
DOI: https://doi.org/10.1134/S0001434613010100
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: M. O. Korpusov, “On the Blow-Up of the Solution of an Equation Related to the Hamilton–Jacobi Equation”, Mat. Zametki, 93:1 (2013), 81–95; Math. Notes, 93:1 (2013), 90–101
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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