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The hyperbolic dirichlet problem

✍ Scribed by R. Pavani; R. Talamo

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
547 KB
Volume
32
Category
Article
ISSN
0895-7177

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✦ Synopsis

The aim of this paper is to take into account the hyperbolic Dirichlet problem on a given transitive curve of the plane. Owing to a representation theorem, we can assume without loss of generality, that our curve is an ellipse. Therefore, given an ellipse and a smooth function on its boundary, we show that there are uncountably many rotations which sssure existence and unicity for the corresponding solution of the hyperbolic Dirichlet problem. Moreover, we give a numerical algorithm for the effective computation of the solution.

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✍ Joseph Bennish πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 224 KB

A hyperbolic mixed initial boundary-value problem is investigated in which the Neumann condition and the Dirichlet condition are given on complementary parts of the boundary. An existence and uniqueness result in Sobolev spaces with additional differentiation in the tangential directions to the inte