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Convergence dans \(L^ p(R^{n+1})\) de la solution de l'équation de Klein-Gordon vers celle de l'équation des ondes. \((L^ p(R^{n+1})\)- convergence of the solution of the Klein-Gordon equation to the solution of the wave equation)

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Názov: Convergence dans \(L^ p(R^{n+1})\) de la solution de l'équation de Klein-Gordon vers celle de l'équation des ondes. \((L^ p(R^{n+1})\)- convergence of the solution of the Klein-Gordon equation to the solution of the wave equation)
Autori: Bachelot, Alain
Informácie o vydavateľovi: Université Paul Sabatier, Faculté des Sciences, Toulouse
Predmety: convergence, Partial differential equations of mathematical physics and other areas of application, continuity of the solution, Klein-Gordon equation, wave equation, inverse scattering problem, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Theoretical approximation in context of PDEs, Second-order nonlinear hyperbolic equations
Popis: We study the continuity of the solution of the Klein-Gordon equation with respect to the mass. We prove the convergence in \(L^ q(R_ t\times R^ n_ x)\) of the solution of the inhomogeneous Klein-Gordon equation to the solution of the wave equation, with same initial data, when the mass tends to 0; we use this result to solve the inverse scattering problem for the equation \[ \square u+m^ 2u=\sum_{k\geq 1}q_ k(x)| u|^{2k}u. \]
Druh dokumentu: Article
Popis súboru: application/xml
DOI: 10.5802/afst.629
Prístupová URL adresa: https://zbmath.org/4052152
Prístupové číslo: edsair.c2b0b933574d..1750280e61b7654440a9b8e05c42c3d7
Databáza: OpenAIRE
Popis
Abstrakt:We study the continuity of the solution of the Klein-Gordon equation with respect to the mass. We prove the convergence in \(L^ q(R_ t\times R^ n_ x)\) of the solution of the inhomogeneous Klein-Gordon equation to the solution of the wave equation, with same initial data, when the mass tends to 0; we use this result to solve the inverse scattering problem for the equation \[ \square u+m^ 2u=\sum_{k\geq 1}q_ k(x)| u|^{2k}u. \]
DOI:10.5802/afst.629