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: II. Potential Theory

Volume and surface potentials arising in Cauchy problems for nonlinear equations in the theory of ion acoustic and drift waves in a plasma are considered, and their properties are examined. For the volume potential, an estimate is derived, which is used to prove a Schauder-type a priori estimate and...

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Veröffentlicht in:Computational mathematics and mathematical physics 2023-02, Vol.63 (2), p.250-284
Hauptverfasser: Korpusov, M. O., Ovsyannikov, E. A.
Format: Artikel
Sprache:eng
Schlagworte:
Acoustic properties
Cauchy problems
Computational Mathematics and Numerical Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Partial Differential Equations
Plasma waves
Potential theory
Wave equations
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Beschreibung
Zusammenfassung:Volume and surface potentials arising in Cauchy problems for nonlinear equations in the theory of ion acoustic and drift waves in a plasma are considered, and their properties are examined. For the volume potential, an estimate is derived, which is used to prove a Schauder-type a priori estimate and Schauder-type estimates for weighted potentials.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523020094