Global existence and asymptotic behaviour of the solution of a generalized burger's equation with viscosity
β Scribed by Hui Zhang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 379 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
We prove the existence and uniqueness of global solutions for the Cauchy problem concerning the evolution equation suggested by the study of plates and beams, where A is a linear operator in a Hilbert space H and M and g are real functions. We also study the asymptotic behaviour of the solutions, u
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
## 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