M. O. Korpusov, A. A. Panin, “Local solvability and solution blowup for the Benjamin–Bona–Mahony–Burgers equation with a nonlocal boundary condition”, TMF, 175:2 (2013), 159–172; Theoret. and Math. Phys., 175:2 (2013), 580

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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 175, Number 2, Pages 159–172
DOI: https://doi.org/10.4213/tmf8417 (Mi tmf8417)

This article is cited in 12 scientific papers (total in 12 papers)

Local solvability and solution blowup for the Benjamin–Bona–Mahony–Burgers equation with a nonlocal boundary condition

M. O. Korpusov, A. A. Panin

Lomonosov Moscow State University, Moscow, Russia

Full-text PDF (432 kB) Citations (12)

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DOI: https://doi.org/10.4213/tmf8417

Abstract: We consider a model initial–boundary value problem for the Benjamin–Bona–Mahony–Burgers equation with initial conditions having a physical meaning. We prove the unique local solvability in the classical sense and obtain sufficient conditions for blowup and an estimate of the blowup time. To prove the blowup, we use the known test function method developed in papers by V. A. Galaktionov, E. L. Mitidieri, and S. I. Pohozaev. We note that this is one of the first results toward the blowup for the considered equation.

Keywords: blowup, local solvability, Benjamin–Bona–Mahony–Burgers equation.

Received: 27.09.2012

English version:
Theoretical and Mathematical Physics, 2013, Volume 175, Issue 2, Pages 580–591
DOI: https://doi.org/10.1007/s11232-013-0047-8

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: M. O. Korpusov, A. A. Panin, “Local solvability and solution blowup for the Benjamin–Bona–Mahony–Burgers equation with a nonlocal boundary condition”, TMF, 175:2 (2013), 159–172; Theoret. and Math. Phys., 175:2 (2013), 580–591

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Linking options:

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https://doi.org/10.4213/tmf8417

https://www.mathnet.ru/eng/tmf/v175/i2/p159

This publication is cited in the following 12 articles:

Alsaedi A., Ahmad B., Kirane M., Torebek B.T., “Blowing-Up Solutions of the Time-Fractional Dispersive Equations”, Adv. Nonlinear Anal., 10:1 (2021), 952–971
M. O. Korpusov, D. K. Yablochkin, “Potential theory and Schauder estimate in Hölder spaces for $(3 + 1)$ -dimensional Benjamin–Bona–Mahoney–Burgers equation”, Comput. Math. Math. Phys., 61:8 (2021), 1289–1314
M. O. Korpusov, E. A. Ovsyannikov, “Blow-up instability in non-linear wave models with distributed parameters”, Izv. Math., 84:3 (2020), 449–501
M. O. Korpusov, “Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source”, Izv. Math., 84:5 (2020), 930–959
I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Math. Notes, 105:5 (2019), 694–706
M. O. Korpusov, D. K. Yablochkin, “Potential theory for a nonlinear equation of the Benjamin–Bona–Mahoney–Burgers type”, Comput. Math. Math. Phys., 59:11 (2019), 1848–1880
M. O. Korpusov, E. V. Yushkov, “Global unsolvability of a nonlinear conductor model in the quasistationary approximation”, Theoret. and Math. Phys., 191:1 (2017), 471–479
A. I. Aristov, “On a Nonlinear Third-Order Equation”, Math. Notes, 102:1 (2017), 3–11
A. A. Panin, G. I. Shlyapugin, “Local solvability and solution blow-up of one-dimensional equations of the Yajima–Oikawa–Satsuma type”, Theoret. and Math. Phys., 193:2 (2017), 1561–1573
E. V. Yushkov, M. O. Korpusov, “Gradient blow-up in generalized Burgers and Boussinesq equations”, Izv. Math., 81:6 (2017), 1286–1296
Korpusov M.O., Lukyanenko D.V., Panin A.A., Yushkov E.V., “Blow-up for one Sobolev problem: Theoretical approach and numerical analysis”, J. Math. Anal. Appl., 442:2 (2016), 451–468
E. V. Yushkov, M. O. Korpusov, “Global Unsolvability of One-Dimensional Problems for Burgers-Type Equations”, Math. Notes, 98:3 (2015), 503–514

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

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