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A. Panin (2015)
On local solvability and blow-up of solutions of an abstract nonlinear Volterra integral equationMathematical Notes, 97
M. Korpusov, S. Mikhailenko (2017)
Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov–Zabolotskaya equationComputational Mathematics and Mathematical Physics, 57
M. Korpusov, D. Lukyanenko, A. Panin, E. Yushkov (2016)
Blow-up for one Sobolev problem: theoretical approach and numerical analysisJournal of Mathematical Analysis and Applications, 442
N.S. Bakhvalov, Ya.M. Zhileikin, E.A. Zabolotskaya (1982)
Sovremennye problemy fiziki. Nelineinaya teoriya zvukovykh puchkov (Contemporary Problems of Physics. Nonlinear Theory of Sound Beams)
(2001)
A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities
(1998)
Novye zadachi matematicheskoi teorii voln (New Problems of Mathematical Theory of Waves)
(1982)
Sovremennye problemy fiziki. Nelineinaya teoriya zvukovykh puchkov (Contemporary Problems of Physics
M. Korpusov (2015)
Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev typeIzvestiya: Mathematics, 79
We consider a problem with some boundary and initial conditions for an equation arising in the theory of ion-sound waves in plasma. We prove that if the spatial (one-dimensional) variable ranges on an interval, then this problem has a unique nonextendable classical solution which in general exists only locally in time. If the spatial variable varies on the half-line, then, for the problem in question, we obtain an upper bound for the lifespan of its weak solution and find initial conditions for which there exist no solutions even locally in time (instantaneous blow-up of the weak solution). A similar result is obtained for the classical solution.
Differential Equations – Springer Journals
Published: Apr 3, 2019
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