On the approximate solution of Dirichlet-type problems with singularities on the boundary
β Scribed by Donald Greenspan; Ralph M. Warten
- Publisher
- Elsevier Science
- Year
- 1962
- Tongue
- English
- Weight
- 563 KB
- Volume
- 273
- Category
- Article
- ISSN
- 0016-0032
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β¦ Synopsis
In the studies of stress, heat flow, fluid flow, potential theory, and electrostatic, magnetostatic, and gravitational fields, there recurs a family of boundary value problems whose associated elliptic partial differential equation has a singular coefficient. This paper presents, in view of modern computational machinery, an effective method for approximating solutions to many such problems.
π SIMILAR VOLUMES
## Abstract For an arbitrary differential operator __P__ of order __p__ on an open set __X__ β R^n^, the Laplacian is defined by Ξ = __P__\*__P__. It is an elliptic differential operator of order __2p__ provided the symbol mapping of __P__ is injective. Let __O__ be a relatively compact domain in _
## Abstract The paper presents existence results for positive solutions of the differential equations __x__ β³ + __ΞΌh__ (__x__) = 0 and __x__ β³ + __ΞΌf__ (__t, x__) = 0 satisfying the Dirichlet boundary conditions. Here __ΞΌ__ is a positive parameter and __h__ and __f__ are singular functions of nonβp
Communicated by B
## Abstract A simpler proof is given of the result of (Whitley and Hromadka II, Numer Methods Partial Differential Eq 21 (2005) 905β917) that, under very mild conditions, any solution to a Dirichlet problem with given continuous boundary data can be approximated by a sum involving a single function