کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4613618 1338768 2006 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Periodic solutions to one-dimensional wave equation with x-dependent coefficients
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Periodic solutions to one-dimensional wave equation with x-dependent coefficients
چکیده انگلیسی

In this paper, we study the nonlinear one-dimensional periodic wave equation with x-dependent coefficients u(x)ytt−(u(x)yx)x+g(x,t,y)=f(x,t) on (0,π)×R under the boundary conditions a1y(0,t)+b1yx(0,t)=0, a2y(π,t)+b2yx(π,t)=0 ( for i=1,2) and the periodic conditions y(x,t+T)=y(x,t), yt(x,t+T)=yt(x,t). Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. A main concept is the notion “weak solution” to be given in Section 2. For T is the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 229, Issue 2, 15 October 2006, Pages 466-493