Potential Theory for a Nonlinear Equation of the Benjamin–Bona–Mahoney–Burgers Type
- 作者: Korpusov M.O.1,2, Yablochkin D.K.1,2
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隶属关系:
- Faculty of Physics, Lomonosov Moscow State University
- RUDN University
- 期: 卷 59, 编号 11 (2019)
- 页面: 1848-1880
- 栏目: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180891
- DOI: https://doi.org/10.1134/S0965542519110071
- ID: 180891
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详细
For the linear part of a nonlinear equation related to the well-known Benjamin–Bona–Mahoney–Burgers (BBMB) equation, a fundamental solution is constructed, which is combined with the second Green formula to obtain a third Green formula in a bounded domain. Then a third Green formula in the entire space is derived by passage to the limit in some class of functions. The properties of the potentials entering the Green formula in the entire space are examined. The Cauchy problem for a nonlinear BBMB-type equation is considered. It is proved that finding its classical solution is equivalent to solving a nonlinear integral equation derived from the third Green formula. The unique local-in-time solvability of this integral equation is proved by applying the contraction mapping principle. Next, the local-in-time classical solvability of the Cauchy problem is proved using the properties of potentials. Finally, the nonlinear capacity method is used to obtain a global-in-time a priori estimate for classical solutions of the Cauchy problem.
作者简介
M. Korpusov
Faculty of Physics, Lomonosov Moscow State University; RUDN University
编辑信件的主要联系方式.
Email: korpusov@gmail.com
俄罗斯联邦, Moscow, 119992; Moscow, 117198
D. Yablochkin
Faculty of Physics, Lomonosov Moscow State University; RUDN University
Email: korpusov@gmail.com
俄罗斯联邦, Moscow, 119992; Moscow, 117198
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