## 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
Numerical Computation of a Cauchy Problem for Laplace's Equation
β Scribed by J. Cheng; Y.C. Hon; T. Wei; M. Yamamoto
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 176 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0044-2267
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## Abstract The nonβcharacteristic Cauchy problem for the heat equation __u__~__xx__~(__x__,__t__) = __u__~1~(__x__,__t__), 0 β©½ __x__ β©½ 1, β β < __t__ < β, __u__(0,__t__) = Ο(__t__), __u__~__x__~(0, __t__) = Ο(__t__), β β < __t__ < β is regularizΓ¨d when approximate expressions for Ο and Ο are given
In this paper the noncharacteristic Cauchy problem NCP u y a x u y b x u y c x u s 0, x g 0, l , t g β«,ήβ¬
Solutions of a class of Cauchy problems are compared with solutions of related perturbed problems. Holder continuous dependence on the perturbation parame-αΊer is established for the difference of these solutions using the logarithmic convexity method. Results are also obtained under weaker restricti