Abstract:
An initial-boundary value problem for plasma ion-sound wave equation is considered. Boltzmann distribution is approximated by a quadratic function. The local (in time) solvability is proved and the analitycal-numerical investigation of the solution's decay is performed for the considered problem. The sufficient conditions for solution's decay and an upper bound of the decay moment are obtained by the test function method. In some numerical examples, the estimation is specified by Richardson's mesh refinement method. The time interval for numerical modelling is chosen according to the decay moment's analytical upper bound. In return, numerical calculations refine the moment and the space-time pattern of the decay. Thus, analytical and numerical parts of the investigation amplify each other.
Keywords:
blow-up; nonlinear initial-boundary value problem; Sobolev type equation; exponential nonlinearity; Richardson extrapolation.
Citation:
M. O. Korpusov, D. V. Lukyanenko, E. A. Ovsyannikov, A. A. Panin, “Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017), 107–123
\Bibitem{KorLukOvs17}
\by M.~O.~Korpusov, D.~V.~Lukyanenko, E.~A.~Ovsyannikov, A.~A.~Panin
\paper Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 2
\pages 107--123
\mathnet{http://mi.mathnet.ru/vyuru376}
\crossref{https://doi.org/10.14529/mmp170209}
\elib{https://elibrary.ru/item.asp?id=29274784}
Linking options:
https://www.mathnet.ru/eng/vyuru376
https://www.mathnet.ru/eng/vyuru/v10/i2/p107
This publication is cited in the following 6 articles:
M. O. Korpusov, A. A. Panin, A. E. Shishkov, “On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type”, Izv. Math., 85:1 (2021), 111–144
M. O. Korpusov, E. A. Ovsyannikov, “Blow-up instability in non-linear wave models with distributed parameters”, Izv. Math., 84:3 (2020), 449–501
M. O. Korpusov, “Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source”, Izv. Math., 84:5 (2020), 930–959
I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Math. Notes, 105:5 (2019), 694–706
M. O. Korpusov, A. K. Matveeva, D. V. Lukyanenko, “Diagnostika mgnovennogo razrusheniya resheniya v nelineinom uravnenii teorii voln v poluprovodnikakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:4 (2019), 104–113
M. O. Korpusov, D. V. Lukyanenko, A. D. Nekrasov, “Analytic-numerical investigation of combustion in a nonlinear medium”, Comput. Math. Math. Phys., 58:9 (2018), 1499–1509
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