Geodesic
Diagnostics of instant decomposition of solution in the nonlinear equation of theory of waves in semiconductors
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 104-113 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers a method for numerical diagnostics of the solution's blow-up in a nonlinear equation of the theory of waves in semiconductors. One feature of the problem under consideration is that there is not even a weak local solution to the problem in time on the positive half-line in spatial variable, while there exists a classical solution local in time in the spatial interval from $0$ to $L$. We numerically show that the lifetime of the solution tends to zero as $L$ tends to infinity. The numerical diagnostics of the solution's blow-up is based on the method of calculating a posterior asymptotically accurate estimate of the error of the obtained numerical solution according to the Richardson extrapolation method.
Keywords: numerical diagnostics of instantaneous solution's blow-up. 
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     title = {Diagnostics of instant decomposition of solution in the nonlinear equation of theory of waves in semiconductors},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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M. O. Korpusov; A. K. Matveeva; D. V. Lukyanenko. Diagnostics of instant decomposition of solution in the nonlinear equation of theory of waves in semiconductors. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 104-113. http://geodesic.mathdoc.fr/item/VYURU_2019_12_4_a7/

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[11] M.O. Korpusov, D.V. Lukyanenko, “Instantaneous Blow-Up Versus Local Solvability for One Problem of Propagation of Nonlinear Waves in Semiconductors”, Journal of Mathematical Analysis and Applications, 459:1 (2018), 159–181 | DOI | MR | Zbl

[12] M.O. Korpusov, D.V. Lukyanenko, A.A. Panin, G.I. Shlyapugin, “On the Blow-Up Phenomena for a One-Dimensional Equation of Ion-Sound Waves in a Plasma: Analytical and Numerical Investigation”, Mathematical Methods in the Applied Sciences, 41:8 (2018), 2906–2929 | DOI | MR | Zbl

[13] Korpusov M. O., Lukyanenko D. V., Panin A. A., Yushkov E. V., “On the Blow-Up of Solutions of a Full Non-Linear Equation That Describes Ion-Sound Waves in Plasma with Non-Coercive Non-Linearities”, Izvestiya. Mathematics, 82:2 (2018), 283–317 | DOI | MR | Zbl

[14] M.O. Korpusov, D.V. Lukyanenko, A.D. Nekrasov, “Analytic-Numerical Investigation of Combustion in a Nonlinear Medium”, Computational Mathematics and Mathematical Physics, 58:9 (2018), 1499–1509 | DOI | MR | Zbl