Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation

DOI10.1080/03605309908821495zbMath0936.35031OpenAlexW1986772858MaRDI QIDQ4719937

Publication date: 30 March 2000

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309908821495

zbMATH Keywords

compatibility conditions small initial data nonlocal term

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Integro-partial differential equations (45K05) Second-order nonlinear hyperbolic equations (35L70)

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Cites Work