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

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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. 
@article{VYURU_2019_12_4_a7,
     author = {M. O. Korpusov and A. K. Matveeva and D. V. Lukyanenko},
     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},
     pages = {104--113},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_4_a7/}
}
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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/