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Local solvability and a priori estimates for classical solutions to an equation of Benjamin-Bona-Mahony-Bürgers type |
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| Authors: | Maxim O Korpusov Dmitry V Lukyanenko Alexander A Panin |
| Institution: | 1. Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow, Russian Federation
S.M. 2. Nikol'skii 3. Mathematical Institute, Peoples' Friendship University of Russia (RUDN University), Moscow, Russian Federation;4. Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow, Russian Federation |
| Abstract: | 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. |
| Keywords: | a priori estimates in context of PDEs blow-up initial value problems for nonlinear higher-order PDEs instantaneous blow-up nonlinear waves |