Progress Report On Contract Da 18 064 Cml 1860 the Formation And Subsequent Beh
Progress Report On Contract Da 18 064 Cml 1860 the Formation And Subsequent Beh
Ignace I Kolodner
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. ; ! , , : . I . • I - 20 - tial equation for the Laplace Transform of u(r, t) = rc(r, t) with res- pect to t, use of the Laplace Transformation seemed to be proper for a problem of this type. Evans, Isaacson and Tic Donald [33], expressed the hope that this technique should produce an elegant solution to their problem, but got nowhere. Likewise, in case of our problem the use of Laplace Transform led to a formal expression for the concen- tration function, which would be the correct expressio...n if the b oundary p were known, but could not be easily used to determine their boundary. (It was realized much later that this expression could be obtained in a simpler way by applying Green's theorem to the function u, see [38]*) What evolved, however, from an interpretation of this formal result, was a basically simple, but very general and powerful method for solving the free boundary value problems for the heat equa- tion, by Folodner [39] . The method consists in a reduction of the q problem to an integro-differential equation for the boundary.
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