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 Tr. Mat. Inst. Steklova, 2008, Volume 260, Pages 213–226 (Mi tm596)

On the Blow-up of Solutions to Nonlinear Initial–Boundary Value Problems

S. I. Pokhozhaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the problem of nonexistence (blow-up) of solutions of nonlinear evolution equations in the case of a bounded (with respect to the space variables) domain. Following the method of nonlinear capacity based on the application of test functions that are optimal (“characteristic”) for the corresponding nonlinear operators, we obtain conditions for the blow-up of solutions to nonlinear initial–boundary value problems. We also show by examples that these conditions are sharp in the class of problems under consideration.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 260, 204–217

Bibliographic databases:

UDC: 517.9
Received in September 2007

Citation: S. I. Pokhozhaev, “On the Blow-up of Solutions to Nonlinear Initial–Boundary Value Problems”, Function theory and nonlinear partial differential equations, Collected papers. Dedicated to Stanislav Ivanovich Pohozaev on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 260, MAIK Nauka/Interperiodica, Moscow, 2008, 213–226; Proc. Steklov Inst. Math., 260 (2008), 204–217

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. P. P. Matus, “Well-posedness of difference schemes for semilinear parabolic equations with weak solutions”, Comput. Math. Math. Phys., 50:12 (2010), 2044–2063
2. E. V. Yushkov, M. O. Korpusov, “Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations”, Math. Notes, 98:3 (2015), 503–514
3. D. A. Schadinskii, “Zakony sokhraneniya i ikh znachenie v razrushenii resheniya v nelineinykh zadachakh dlya parabolicheskikh uravnenii”, Tr. In-ta matem., 23:2 (2015), 103–111
4. Matus P.P., Churbanova N.G., Shchadinskii D.A., “On the role of conservation laws and input data in the generation of peaking modes in quasilinear multidimensional parabolic equations with nonlinear source and in their approximations”, Differ. Equ., 52:7 (2016), 942–950
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