The amount of non-uniqueness for factored equations with Euler-Poisson-Darboux factors
✍ Scribed by Jerome A. Goldstein; James H. Lightbourne III; James T. Sandefur Jr.
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 103 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
Communicated by G. F. Roach Of concern are factored Euler-Poisson-Darboux equations of the type , H (d/dt#( /t)d/dt#A H )u(t)"0, where, for example, A H "!c H , being the Dirichlet Laplacian acting on ¸( ), L1L, and 0(c (2(c , . More generally !A H can be the square of the generator of a (C
) group on a Banach space. When the constant is negative, the initial value problem for the factored EPD equation is ill-posed. Nevertheless, we determine how many initial conditions are necessary to guarantee uniqueness of a solution. This number jumps up as crosses a negative integer from right to left.