Regularity of the Solution of the First Initial-Boundary Value Problem for Hyperbolic Equations in Domains with Cuspidal Points on Boundary

Nguyen Manh Hung,Vu Trong Luong

doi:10.1155/2009/135730

Abstract

The goal of this paper is to establish the regularity of the solution of the first initial-boundary value problem for general higher-order hyperbolic equations in cylinders with the bases containing cuspidal points.

Highlights

Initial boundary-value problems for hyperbolic and parabolic type equations in a cylinder with the base containing conical points have been developed sufficiently by us 1–4, the main results of which are about the unique existence of the solution and asymptotic expansions of the solution near a neighborhood of a conical point
We are concerned with the first initial boundary value problems for higher hyperbolic equation in a cylinder, whose base containing cuspidal points
In 5, 6 we showed the existence of a sequence of smooth domains {Ω } >0 such that Ω ⊂ Ω and lim → 0Ω Ω

Summary

Introduction

Initial boundary-value problems for hyperbolic and parabolic type equations in a cylinder with the base containing conical points have been developed sufficiently by us 1–4 , the main results of which are about the unique existence of the solution and asymptotic expansions of the solution near a neighborhood of a conical point. Those problems mentioned above in cylinder with base containing cuspidal point, interesting for applied sciences, have not been studied yet.

Cusp Domain and Weighted Sobolev Spaces

Formulation of the Problem

The Main Results

L2 QT ft

L2 Ω utt

Examples