THE CAUCHY PROBLEM FOR AN NONLINEAR WAVE EQUATION

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Аннотация

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.

Авторлар туралы

M. Artemeva

Lomonosov Moscow State University; People Friendship University of Russia named after Patrice Lumumba

Email: artemeva.mv14@physics.msu.ru
Москва

M. Korpusov

Lomonosov Moscow State University; People Friendship University of Russia named after Patrice Lumumba

Email: korpusov@gmail.com
Russia

Әдебиет тізімі

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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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