On certain global solutions of the Cauchy problem for the (classical) coupled Klein-Gordon-Dirac equations in one and three space dimensions
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Publication:1845014
DOI10.1007/BF00250789zbMath0285.35042OpenAlexW2005963734MaRDI QIDQ1845014
John M. Chadam, Robert T. Glassey
Publication date: 1974
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00250789
Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Initial value problems for second-order hyperbolic equations (35L15) Qualitative properties of solutions to partial differential equations (35B99)
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Cites Work
- Unnamed Item
- Unnamed Item
- Decay and asymptotics for \(\square u = F(u)\)
- Non-linear semi-groups
- Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
- On solutions of nonlinear wave equations
- The cauchy problem for the coupled maxwell and dirac equations
- On the Cauchy Problem for the Coupled Maxwell-Dirac Equations
- Properties of the Solutions of the Cauchy Problem for the (Classical) Coupled Maxwell-Dirac Equations in One Space Dimension
- On the Asymptotic Behavior of Nonlinear Wave Equations
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