کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4613634 1338771 2006 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Smooth solutions to a class of quasilinear wave equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Smooth solutions to a class of quasilinear wave equations
چکیده انگلیسی

This article investigates the existence/nonexistence of smooth solutions of nonlinear vibration equations which arise from the one-dimensional motion of polytropic gas without external forces contained in a finite interval. For any fixed arbitrarily long time, we show that there are smooth small amplitude solutions of the nonlinear equations for which the periodic solutions of the linearized equation are the first-order approximations. On the other hand, when the nonlinearity is strictly convex or concave, there exists no time-periodic solutions which are twice continuously differentiable. An example of possible singularities which occur at the second derivatives is illustrated. We also give another kind of exact solutions with singularity such that shocks occur after a finite time. Furthermore, we get an estimate of the life span of smooth solutions to the initial-boundary value problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 224, Issue 2, 15 May 2006, Pages 229-257