When b s 0, Eq. 1.1 becomes usual semilinear wave equations. When ลฝ . b)0, we call Eq. 1.1 wave equations of Kirchhoff type which have been introduced in order to study the nonlinear vibrations of an elastic string by
Global Solution of a Nonlinear String Equation
โ Scribed by W.G. Newman
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 351 KB
- Volume
- 192
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We study the boundedness and a priori bounds of global solutions of the problem u"0 in ;(0, ยน ), j S j R # j S j "h(u) on j ;(0, ยน ), where is a bounded domain in 1,, is the outer normal on j and h is a superlinear function. As an application of our results we show the existence of sign-changing sta
The existence, uniqueness, and L ฯฑ estimate of the weak solution to the initial boundary value problem for the doubly nonlinear parabolic equation ลฝ . t with zero boundary condition in a bounded domain โ ; R N are established. In particular, the behavior of the solution as t ยช 0 q and t ยช qฯฑ is in