The hyperbolic semilinear initial value problem \(\varepsilon u_{t}+A u_{1}+B u+f(u)=0\), \(u(0)=u_{0,}, u_{t}(0)=u_{1 s}\), with commuting positive selfadjoint operators \(A\) and \(B\) in a Hilbert space \(X\) is considered. The term \(A u\), is a damping term. It is shown that the solutions conve
β¦ LIBER β¦
Singularities of semilinear waves
β Scribed by Joseph B. Keller; Lu Ting
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 571 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0010-3640
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The existence of positive solutions of a second order differential equation of the form z"+ g(t) f (z)=0 (1.1) with suitable boundary conditions has proved to be important in theory and applications whether g is continuous in [0, 1] or g has singularities. These equations often arise in the study