Abstract
Three Cauchy problems for Sobolev-type equations with a common linear part from the theory of ion acoustic and drift waves in a plasma are considered. The problems are reduced to equivalent integral equations. We prove the existence of unextendable solutions for two problems and the existence of a local-in-time solution for the third problem. For one of the problems, by applying a modified method of Kh.A. Levin, sufficient conditions for finite time blow-up of solutions are obtained and an upper bound for the solution blow-up time is found. For another problem, S.I. Pohozaev’s nonlinear capacity method is used to obtain a finite time blow-up result and two results concerning the nonexistence of even local solutions, and an upper bound for the solution blow-up time is obtained as well.
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REFERENCES
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Funding
This work was supported by the Foundation for Advancement of Theoretical Physics and Mathematics “BASIS” and by the Program of Strategic Academic Leadership of RUDN University.
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Translated by I. Ruzanova
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Korpusov, M.O., Ovsyannikov, E.A. Local Solvability, Blow-Up, and Hölder Regularity of Solutions to Some Cauchy Problems for Nonlinear Plasma Wave Equations: III. Cauchy Problems. Comput. Math. and Math. Phys. 63, 1218–1236 (2023). https://doi.org/10.1134/S0965542523070072
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DOI: https://doi.org/10.1134/S0965542523070072