We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la
Solutions and linearization of the nonlinear dynamics of radiation damping
β Scribed by Rourke, David E.
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 278 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1043-7347
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π SIMILAR VOLUMES
A functional analysis method is used to prove the existence and the uniqueness of solutions of a class of linear and nonlinear functional equations in the Hilbert Ε½ . Ε½ . space H β¬ and the Banach space H β¬ . In the case of the nonlinear functional 2 1 equation, a bound of the solution is also given.
This paper studies the Cauchy problem of the 3D NavierβStokes equations with nonlinear damping termβ|β__u__β|β^__Ξ²__β1^__u__ (__Ξ²__ββ₯β1). For __Ξ²__ββ₯β3, we derive a decay rate of the __L__^2^βnorm of the solutions. Then, the large time behavior is given by comparing the equation with the classic 3D