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Global existence and stability for wave equation of Kirchhoff type with memory condition at the boundary

โœ Scribed by M.L. Santos; J. Ferreira; D.C. Pereira; C.A. Raposo

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
243 KB
Volume
54
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

We consider a nonlinear wave equation of Kirchho type with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

๐Ÿ“œ SIMILAR VOLUMES

Global existence, asymptotic behaviour,
Global existence, asymptotic behaviour, and global non-existence of solutions for damped non-linear wave equations of Kirchhoff type in the whole space
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We study the global existence, asymptotic behaviour, and global non-existence (blow-up) of solutions for the damped non-linear wave equation of Kirchho! type in the whole space: , and '0, with initial data u(x, 0)"u (x) and u R (x, 0)"u (x).

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We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation: When the initial energy associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties.