On the blow‐up phenomena for a 1‐dimensional equation of ion sound waves in a plasma: Analytical and numerical investigation

DOI10.1002/MMA.4791zbMath1448.35055OpenAlexW2789746713MaRDI QIDQ4576935

G. I. Shlyapugin, M. O. Korpusov, A. A. Panin, Dmitry V. Lukyanenko

Publication date: 11 July 2018

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.4791

zbMATH Keywords

method of test functions contracting mapping nonextendable solution numerical blow-up diagnostics ion sound waves in plasma

Mathematics Subject Classification ID

Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Blow-up in context of PDEs (35B44) Initial-boundary value problems for nonlinear higher-order PDEs (35G31)

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Local solvability and global unsolvability of a model of ion-sound waves in a plasma ⋮ Analytical-numerical study of finite-time blow-up of the solution to the initial-boundary value problem for the nonlinear Klein-Gordon equation ⋮ Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source ⋮ Blow-up instability in non-linear wave models with distributed parameters ⋮ Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations. I: Green formulas ⋮ On nonextendable solutions and blow-ups of solutions of pseudoparabolic equations with coercive and constant-sign nonlinearities: analytical and numerical study ⋮ On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type

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