Geodesic
Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 2, pp. 107-123

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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. 
@article{VYURU_2017_10_2_a8,
     author = {M. O. Korpusov and D. V. Lukyanenko and E. A. Ovsyannikov and A. A. Panin},
     title = {Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {107--123},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_2_a8/}
}
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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 Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 2, pp. 107-123. http://geodesic.mathdoc.fr/item/VYURU_2017_10_2_a8/