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Local solvability and a priori estimates for classical solutions to an equation of Benjamin‐Bona‐Mahony‐Bürgers type
Author(s) -
Korpusov Maxim O.,
Lukyanenko Dmitry V.,
Panin Alexander A.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6657
Subject(s) - mathematics , a priori and a posteriori , type (biology) , mathematical analysis , initial value problem , cauchy distribution , nonlinear system , boundary value problem , half line , cauchy problem , a priori estimate , ecology , philosophy , epistemology , biology , physics , quantum mechanics
We establish the local (in time) solvability in the classical sense for the Cauchy problem and first and second boundary‐value problems on the half‐line for a nonlinear equation similar to Benjamin‐Bona‐Mahony‐Bürgers‐type equation. We also derive an a priori estimate that implies sufficient blow‐up conditions for the second boundary‐value problem. We obtain analytically an upper bound of the blow‐up time and refine it numerically using Richardson effective accuracy order technique.