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Izvestiya: Mathematics, 2017, Volume 81, Issue 6, Pages 1286–1296
DOI: https://doi.org/10.1070/IM8471 (Mi im8471) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Gradient blow-up in generalized Burgers and Boussinesq equations

E. V. Yushkov, M. O. Korpusov

Lomonosov Moscow State University, Faculty of Physics
English version PDF (219 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM8471
Abstract: We study the influence of gradient non-linearity on the global solubility of initial-boundary value problems for a generalized Burgers equation and an improved Boussinesq equation which are used for describing one-dimensional wave processes in dissipative and dispersive media. For a large class of initial data, we obtain sufficient conditions for global insolubility and a bound for blow-up times. Using the Boussinesq equation as an example, we suggest a modification of the method of non-linear capacity which is convenient from a practical point of view and enables us to estimate the blow-up rate. We use the method of contraction mappings to study the possibility of instantaneous blow-up and short-time existence of solutions.
Keywords: gradient non-linearity, Burgers equation and generalized Boussinesq equations, blow-up phenomena, method of non-linear capacity.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12460
This paper was written with the support of the Russian Foundation for Basic Research (grant no. 13-01-12460).
Received: 12.11.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2017, Volume 81, Issue 6, Pages 232–242
DOI: https://doi.org/10.4213/im8471
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 35B44, 35A01, 35G31
Language: English
Original paper language: Russian
Citation: E. V. Yushkov, M. O. Korpusov, “Gradient blow-up in generalized Burgers and Boussinesq equations”, Izv. RAN. Ser. Mat., 81:6 (2017), 232–242; Izv. Math., 81:6 (2017), 1286–1296
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:279
    English version PDF:28
    References:89
    First page:60
     
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