Uniqueness and convergence of numerical solution of the cauchy problem for the laplace equation by a charge simulation method
β Scribed by Takashi Ohe; Kohzaburo Ohnaka
- Publisher
- Japan Society for Industrial and Applied Mathematics
- Year
- 2004
- Tongue
- English
- Weight
- 830 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0916-7005
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π SIMILAR VOLUMES
We consider the Cauchy problem for the Laplace equation in the half plane x > 0 where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 < x < 1. This is a model ill-posed problem since a small perturbation in the initial data leads to large errors in the solution. We use
## Communicated by G. F. Roach We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for
## Abstract Let __D__ β β^__n__^ be a bounded domain with piecewiseβsmooth boundary, and __q__(__x__,__t__) a smooth function on __D__ Γ [0, __T__]. Consider the timeβlike Cauchy problem magnified image magnified image Given __g__, __h__ for which the equation has a solution, we show how to approxi