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This article is cited in 3 scientific papers (total in 3 papers)
On an instantaneous blow-up of solutions of evolutionary problems on the half-line
M. O. Korpusov Faculty of Physics, Lomonosov Moscow State University
Abstract:
We consider some initial-boundary value problems
on the half-line for ‘1+1’-dimensional equations
of Sobolev type with homogeneous boundary conditions
at the beginning of the half-line. We show that weak
solutions of these problems are absent even locally in time.
Moreover, we consider problems on an interval with the
same boundary conditions on one of the ends of the
interval $[0,L]$. We prove the local in time (unique)
solubility of the problems under consideration in the
classical sense, and obtain sufficient conditions
for the blow-up of these solutions in finite time.
Using the upper bounds thus obtained for the blow-up times
for classical solutions of the corresponding problems,
we show that the blow-up time tends to zero as $L\to+\infty$.
Thus, a classical solution on the line is also
absent, even locally, and we describe an algorithm
for the subsequent numerical diagnosis of the instantaneous
blow-up on the half-line.
Keywords:
non-linear equations of Sobolev type, blow-up, local solubility,
non-linear capacity, bounds for the blow-up time.
Received: 10.04.2017
Citation:
M. O. Korpusov, “On an instantaneous blow-up of solutions of evolutionary problems on the half-line”, Izv. Math., 82:5 (2018), 914–930
Linking options:
https://www.mathnet.ru/eng/im8684https://doi.org/10.1070/IM8684 https://www.mathnet.ru/eng/im/v82/i5/p61
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Abstract page: | 437 | Russian version PDF: | 70 | English version PDF: | 24 | References: | 63 | First page: | 27 |
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