Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations. I: Green formulas

DOI10.1134/S096554252209007XzbMath1500.35238OpenAlexW4307109239MaRDI QIDQ2090299

M. O. Korpusov, E. A. Ovsyannikov

Publication date: 25 October 2022

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s096554252209007x

zbMATH Keywords

fundamental solutionGreen formulasnonlinear Sobolev-type equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Fundamental solutions to PDEs (35A08) Hydro- and aero-acoustics (76Q05) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (2)

Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations. II: Potential theory ⋮ Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations. III: Cauchy problems

Cites Work

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• Blow-up for one Sobolev problem: theoretical approach and numerical analysis
• On the nonextendable solution and blow-up of the solution of the one-dimensional equation of ion-sound waves in a plasma
• Fundamental solutions of Sobolev-type operators and some initial boundary-value problems
• Instantaneous blow-up versus local solvability for one problem of propagation of nonlinear waves in semiconductors
• Local solvability and solution blow-up of one-dimensional equations of the Yajima-Oikawa-Satsuma type
• Nonlinear equations of the theory of ion-sound plasma waves
• Blow-up of solutions of nonclassical nonlocal nonlinear model equations
• Blow-up phenomena in the model of a space charge stratification in semiconductors: analytical and numerical analysis
• Blow-up in Nonlinear Sobolev Type Equations
• Blow-up instability in non-linear wave models with distributed parameters
• The equation and several problems associated with it
• POTENTIAL THEORY FOR THE EQUATION OF SMALL OSCILLATIONS OF A ROTATING FLUID
• Blow-up of solutions of a full non-linear equation of ion-sound waves in a plasma with non-coercive non-linearities
• On the blow‐up phenomena for a 1‐dimensional equation of ion sound waves in a plasma: Analytical and numerical investigation
• Blow-Up in Nonlinear Equations of Mathematical Physics
• NONCLASSICAL EQUATIONS OF MATHEMATICAL PHYSICS. LINEAR SOBOLEV TYPE EQUATIONS OF HIGHER ORDER
• Local Solvability and Decay of the Solution of an Equation with Quadratic Noncoercive Nonlineatity
• Asymptotic expansions for a model with distinguished “fast” and “slow” variables, described by a system of singularly perturbed stochastic differential equations
• Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source
• Unsteady waves in anisotropic dispersive media

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