Global solutions for dissipative Kirchhoff strings with \(m(r)=r^p\) \((p<1)\)

DOI10.1006/jmaa.2000.6958zbMath0973.35139OpenAlexW1984731873MaRDI QIDQ1588419

Marina Ghisi

Publication date: 14 November 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6958

zbMATH Keywords

asymptotic behaviourglobal existencesmall initial dataKirchhoff equationspolynomial decaydissipative operatorsnonlocal nonlinearities

Mathematics Subject Classification ID

Degenerate hyperbolic equations (35L80) Abstract hyperbolic equations (35L90) Strings (74K05)

Related Items (4)

Global solutions for dissipative Kirchhoff strings with non-Lipschitz nonlinear term ⋮ Existence, uniqueness, and exponential stability for the Kirchhoff equation in whole hyperbolic space ⋮ Well-posedness and stability for Kirchhoff equation with non-porous acoustic boundary conditions ⋮ Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay

Cites Work

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• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• Scattering for a quasilinear hyperbolic equation of Kirchhoff type
• Global existence for abstract evolution equations of weakly hyperbolic type
• Decay estimates for the generalized damped extensible string and beam equations
• The initial value problem for a stretched string
• On some quasilinear wave equations with dissipative terms
• Nonlinear perturbations of the kirchhoff equation
• The Cauchy problem for Kirchhoff equations

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