Enviar artigo por via de e-mail THE CAUCHY PROBLEM FOR AN NONLINEAR WAVE EQUATION
- Autores: Artemeva M.V1,2, Korpusov M.O1,2
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Afiliações:
- Lomonosov Moscow State University
- People Friendship University of Russia named after Patrice Lumumba
- Edição: Volume 60, Nº 10 (2024)
- Páginas: 1299-1311
- Seção: PARTIAL DERIVATIVE EQUATIONS
- URL: https://ogarev-online.ru/0374-0641/article/view/270535
- DOI: https://doi.org/10.31857/S0374064124100014
- EDN: https://elibrary.ru/JUDMOQ
- ID: 270535
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Texto integral
Resumo
A heat-electric (1+ 1)-dimensional model of semiconductor heating in an electric field is considered. For the corresponding Cauchy problem, the existence of a classical solution that is short-lived in time is proved, a global a priori estimate is obtained in time, and a result is obtained about the absence of even a classical solution local in time.
Sobre autores
M. Artemeva
Lomonosov Moscow State University; People Friendship University of Russia named after Patrice Lumumba
Email: artemeva.mv14@physics.msu.ru
M. Korpusov
Lomonosov Moscow State University; People Friendship University of Russia named after Patrice Lumumba
Email: korpusov@gmail.com
Russia
Bibliografia
- Tymoshenko, A.V., Kalyaev, D.V., Perlov, A.Yu. [et al.], Comparative analysis of analytical and empirical methods of assessment of radar monitoring systems current reliability parameters, Proc. of univ. Electronics, 2020, vol. 25, no. 3, pp. 244–254.
- Korpusov, M.O., On the blow-up of the solution of an equation related to the Hamilton–Jacobi equation, Math. Notes, 2013, vol. 93, pp. 90–101.
- Korpusov, M.O., The destruction of the solution of the nonlocal equation with gradient nonlinearity, Bull. South Ural State Univ. Ser. Math. Modelling, Programming & Comp. Software, 2012, vol. 11, pp. 45–53.
- Korpusov, M.O., Panin, A.A., and Shishkov, A.E., On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type, Izvestiya: Mathematics, 2021, vol. 85, no. 1, pp. 111–144.
- Korpusov, M.O., Perlov, A.Yu., Tymoshenko, A.V., and Shafir, R.S., On the blow-up of the solution of a nonlinear system of equations of a thermal-electrical model, Math. Notes, 2023, vol. 114, no. 5, pp. 850–861.
- Korpusov, M.O., Perlov, A.Yu., Tymoshenko, A.V., and Shafir, R.S., Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity, Theor. Math. Phys., 2023, vol. 217, no. 2, pp. 1743–1754.
- Panin, A.A., On local solvability and blow-up of solutions of an abstract nonlinear Volterra integral equation, Math. Notes, 2015, vol. 97, no. 6, pp. 892–908.
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