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TMF, 2013, Volume 177, Number 1, Pages 93–110 (Mi tmf8507)  

This article is cited in 2 scientific papers (total in 2 papers)

Local solvability and blowup of the solution of the Rosenau–Bürgers equation with different boundary conditions

A. A. Panin

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider several models of initial boundary-value problems for the Rosenau–Bürgers equation with different boundary conditions. For each of the problems, we prove the unique local solvability in the classical sense, obtain a sufficient condition for the blowup regime, and estimate the time of the solution decay. The proof is based on the well-known test-function method.

Keywords: blowup regime, local solvability, noncontinuable solution, Rosenau–Bürgers equation

DOI: https://doi.org/10.4213/tmf8507

Full text: PDF file (467 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 177:1, 1361–1376

Bibliographic databases:

Received: 29.01.2013

Citation: A. A. Panin, “Local solvability and blowup of the solution of the Rosenau–Bürgers equation with different boundary conditions”, TMF, 177:1 (2013), 93–110; Theoret. and Math. Phys., 177:1 (2013), 1361–1376

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v177/i1/p93

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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. E. V. Yushkov, M. O. Korpusov, “Gradient blow-up in generalized Burgers and Boussinesq equations”, Izv. Math., 81:6 (2017), 1286–1296  mathnet  crossref  crossref  adsnasa  isi  elib
    2. I. I. Kolotov, A. A. Panin, “O neprodolzhaemykh resheniyakh i razrushenii reshenii psevdoparabolicheskikh uravnenii s koertsitivnoi i znakopostoyannoi nelineinostyami: analiticheskoe i chislennoe issledovanie”, Matem. zametki, 105:5 (2019), 708–723  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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