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

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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 12 scientific papers (total in 12 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 (12)

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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

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Linking options:

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https://doi.org/10.4213/mzm8955

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This publication is cited in the following 12 articles:

M. V. Artemeva, M. O. Korpusov, A. A. Panin, “On the solvability of the Cauchy problem for a thermal–electrical model”, Theoret. and Math. Phys., 222:2 (2025), 183–197
M. V. Artemeva, M. O. Korpusov, “On the Existence of a Nonextendable Solution of the Cauchy problem for a $(1+1)$-Dimensional Thermal-Electrical Model”, Math. Notes, 115:5 (2024), 653–663
M. V. Artemeva, M. O. Korpusov, “On the blow-up of the solution of a $(1+1)$-dimensional thermal–electrical model”, Theoret. and Math. Phys., 219:2 (2024), 748–760
A. A. Kon'kov, A. E. Shishkov, “On global solutions of second-order quasilinear elliptic inequalities”, Math. Notes, 116:5 (2024), 1014–1019
M. V Artemeva, M. O Korpusov, “THE CAUCHY PROBLEM FOR AN NONLINEAR WAVE EQUATION”, Differencialʹnye uravneniâ, 60:10 (2024), 1299
M. V. Artemeva, M. O. Korpusov, “On the existence of a nonextendable solution of the Cauchy problem for a $(3+1)$-dimensional thermal–electrical model”, Theoret. and Math. Phys., 221:3 (2024), 2207–2218
M. V. Artemeva, M. O. Korpusov, “The Cauchy Problem for a Nonlinear Wave Equation”, Diff Equat, 60:10 (2024), 1369
M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity”, Theoret. and Math. Phys., 217:2 (2023), 1743–1754
M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model”, Math. Notes, 114:5 (2023), 850–861
Ivan E. Egorov, Sergey V. Popov, PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'19), 2172, PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'19), 2019, 030008
B. Ahmad, A. Alsaedi, M. Kirane, “Nonexistence results for the Cauchy problem of time fractional nonlinear systems of thermo-elasticity”, Math. Meth. Appl. Sci., 40:12 (2017), 4272–4279
M. Boutefnouchet, H. Erjaee, M. Kirane, M. Qafsaoui, “Nonexistence results for the Cauchy problem for some fractional nonlinear systems of thermo-elasticity type”, ZAMM-Z. Angew. Math. Mech., 96:9 (2016), 1119–1128

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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