## Abstract The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form __u__β²(__t__)= β __Au__(__t__) + __M__(__u__(__t__)) is shown. Here __A__ is a closed, positive definite, selfβadjoint linear operator with domain __D__(__A__) dense in a Hilbert spac
Generalized Solutions to Fifth-Order Evolution Equations
β Scribed by M.M. Melo
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 147 KB
- Volume
- 259
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
I obtain results of existence and uniqueness of generalized solutions for the Cauchy problem to fifth-order evolution equations such as third member of Kortewegαde Vries hierarchy, Olver, Benney, and Fisher equations. I show that my results are associated with the solution obtained by Ponce.
π SIMILAR VOLUMES
The explicit closed-form solutions for a second-order differential equation with a constant self-adjoint positive definite operator coefficient A (the hyperbolic case) and for the abstract Euler-Poisson-Darboux equation in a Hilbert space are presented. On the basis of these representations, we prop