In this paper we study the generalized Burgers equation u t + (u 2 /2) x = f (t)u xx , where f (t) > 0 for t > 0. We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to L β (R), as well it is o
Existence and convergence of solutions for the generalized BBM-Burgers equations with dissipative term
β Scribed by Huijiang Zhao; Benjin Xuan
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 645 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
We obtain the global existence and uniqueness for a generalized Burger's equation with viscosity and the initial value being in L °° by successive method. Moreover, under certain condition on the initial value the solution tends to the solution of a linear heat equation in H 1.
## Abstract We study the Cauchy problem of nonlinear KleinβGordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a s
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