The Exterior Tricomi and Frankl Problem
Received:February 12, 1989  
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Fund Project:This research work was supported by the Foundations C.A.P.E.S.(Coordenacao de Aperfercoamento do Pessoal de Ensino Superior) and F.I.N.E.P.(Finan ciadora de Estudos e Projetos) and by the Institute of Mathematical Sciences of Sao Carlos. University of Sao Paulo.
Author NameAffiliation
John M. Rassias The American College of Greece 
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      F. G. Tricomi (1923- ), S. Gellerstedt (1935- ), F. I . Frankl (1945- ), A. V. Bitsadze and M. A. Lavrentiev (1950- ), M. H. Protter (1953- ) and most of the recent workers in the field of mixed type boundary value problems have considered only one parabolic line of degeneracy. The problem with more than one parabolic line of degeneracy becomes more complicated. The above researchers and many others have restricted their attention to the Chaplygin equation:K(y)·uxx uyy =f(x,y) and not considered the "generalized Chaplygin equation:"Lu=K(y)·uxx uyy r(x,y)·u=f(x,y) because of the difficulties that arise when r1=non-trivial(≠0). Also it is unusual for anyone to study such problems in a doubly connected region. In this paper 1 consider a case of this type with two parabolic lines of degeneracy, r2=non-trivial(≠0).in a doubly connected region, and such that boundary conditions are prescribed only on the-exterior boundary" of the mixed domain, and 1 obtain umqueness results for quasnegutar solutions of the characteristic and non-characteristic Problem by applying the b,c energy integral method in the mixed domain.
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