On the existence of solutions for some nondegenerate nonlinear wave equations of Kirchhoff type

Title:

On the existence of solutions for some nondegenerate nonlinear wave equations of Kirchhoff type

Creator:

Jong Yeoul and Bae, Jeong Ja

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:eecee36b-7f15-4eb7-b049-80b52745cc81
uuid:eecee36b-7f15-4eb7-b049-80b52745cc81

Subject:

existence and uniqueness, Galerkin method, and nondegenerate wave equation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $\Omega $ be a bounded domain in ${\mathbb{R}}^n$ with a smooth boundary $\Gamma $. In this work we study the existence of solutions for the following boundary value problem: \[ \frac{\partial ^2 y}{\partial t^2}-M\biggl (\int _\Omega |\nabla y|^2\mathrm{d}x\biggr ) \Delta y -\frac{\partial }{\partial t}\Delta y=f(y) \quad \text{in} Q=\Omega \times (0,\infty ),.1 y=0 \quad \text{in} \Sigma _1=\Gamma _{\!1} \times (0,\infty ), M\biggl (\int _\Omega |\nabla y|^2\mathrm{d}x\biggr ) \frac{\partial y}{\partial \nu } +\frac{\partial }{\partial t}\Bigl (\frac{\partial y}{\partial \nu }\Bigr )=g \quad \text{in} \Sigma _0=\Gamma _{\!0} \times (0,\infty ), y(0)=y_0,\quad \frac{\partial y}{\partial t}\,(0)=y_1 \quad \text{in} \quad \Omega , \qquad \mathrm{(1)}\] where $M$ is a $C^1$-function such that $M(\lambda ) \ge \lambda _0 >0$ for every $\lambda \ge 0$ and $f(y)=|y|^\alpha y$ for $\alpha \ge 0$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

781-795

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:4

Harvested from:

CDK

Metadata only:

false