On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions (Q1779351)
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scientific article; zbMATH DE number 2173097
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions |
scientific article; zbMATH DE number 2173097 |
Statements
On the nonlinear wave equation \(u_{tt}-B(t,\| u \|^2, \| u_x\|^2)u_{xx}=f(x,t,u,u_x,u_t,\| u\|^2,\| u_x\|^2)\) associated with the mixed homogeneous conditions (English)
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1 June 2005
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An initial boundary value problem in a cylinder with mixed boundary conditions for the Kirchhoff type equation is considered. The author gives sufficient conditions under which the problem in question has a unique local weak solution. To obtain this result, a linear recurrent procedure and compactness arguments are exploited.
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Kirchhoff equation
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existence
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mixed boundary conditions
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unique local weak solution
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0.99849504
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0.99445885
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0.9919088
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0.98889136
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0.9343162
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0.8933591
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0.88890034
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