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On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type

Authors:

Jong Yeoul Park Jeong Ja Bae

Affiliation:

(1) Department of Mathematics, Pusan National University, Pusan, 609-735, Korea

Abstract:

Let

be a bounded domain in #x211D;ⁿ with a smooth boundary Gamma

. In this work we study the existence of solutions for the following boundary value problem:

$begin{gathered}frac{{partial ^2 y}}{{partial t^2 }} - Mleft( {int_Omega {left| {nabla y} right|^2 dx} } right)Delta y - frac{partial }{{partial t}}Delta y = fleft( y right)inQ = Omega times left( {0,infty } right), hfill y = 0insum _0 = Gamma _0 times left( {0,infty} right), hfill Mleft( {int_Omega {left| {nabla y} right|^2 dx}} right)frac{{partial y}}{{partial nu }} + frac{partial }{{partial t}}left( {frac{{partial y}}{{partial nu }}} right) = ginsum _0 = Gamma _0 times left( {0,infty } right), hfill yleft( 0 right) = y_0 frac{partial }{{partial t}}left( 0 right) = y1,inOmega , hfill end{gathered}$

where M is a C¹-function such that M( lambda

)

₀ > 0 for every lambda

0 and f(y) = |y|y for agr

Keywords:

existence and uniqueness Galerkin method nondegenerate wave equation

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