On the nonlinear wave equation \(u_{tt}-B(t,\|u\|^2, \|u_{x}\|^2, \|u_t\|^2)u_{xx}= f(x,t,u,u_x,u_t,\|u\|^2,\|u_x\|^2,\|u_t\|^2)\) associated with mixed homogeneous conditions. (Q1883106)
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 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the nonlinear wave equation \(u_{tt}-B(t,\|u\|^2, \|u_{x}\|^2, \|u_t\|^2)u_{xx}= f(x,t,u,u_x,u_t,\|u\|^2,\|u_x\|^2,\|u_t\|^2)\) associated with mixed homogeneous conditions. |
scientific article; zbMATH DE number 2105456
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the nonlinear wave equation \(u_{tt}-B(t,\|u\|^2, \|u_{x}\|^2, \|u_t\|^2)u_{xx}= f(x,t,u,u_x,u_t,\|u\|^2,\|u_x\|^2,\|u_t\|^2)\) associated with mixed homogeneous conditions. |
scientific article; zbMATH DE number 2105456 |
Statements
On the nonlinear wave equation \(u_{tt}-B(t,\|u\|^2, \|u_{x}\|^2, \|u_t\|^2)u_{xx}= f(x,t,u,u_x,u_t,\|u\|^2,\|u_x\|^2,\|u_t\|^2)\) associated with mixed homogeneous conditions. (English)
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1 October 2004
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The authors consider a mixed problem for a one-dimensional quasilinear hyperbolic equation of the Kirchhoff type with a semilinear right-hand side. A linear recursive scheme is proposed which leads to the local existence theorem. Also an asymptotic expansion is obtained for a perturbed semilinear part of the equation.
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Kirchhoff equation
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semilinear right-hand side
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linear recursive scheme
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one space dimension
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0.99445885
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0.99330795
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0.9923719
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0.98668724
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0.9809735
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0.92479175
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0.89207524
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0.88289654
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