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Register a new userExistence And Uniqueness Of Strong Solution For A Semi- Linear Wave Equation With Nonlinear Boundary Dissipation
وجود و وحدانية حل قوي للمعادلة الموجية شبه الخطية مع شرط التبدد الحدي اللاخطي
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وديع علي( باحث )
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نهدف في هذا البحث إلى إثبات وجود و وحدانية حل قوي لمسألة القيم الحدية الابتدائية للمعادلة الموجية شبه الخطية مع شرط التبدد الحدي اللاخطي، بتحويلها إلى مسألة كوشي ذات معادلة تفاضلية مؤثرية من المرتبة الثانية في فضاء هلبرت، و ذلك باستخدام صيغة غرين لثلاثية من فضاءات هلبرت.
We aim in this research to study the existence and uniqueness of strong solution for initial-boundary values problem for a semi-linear wave equation with the nonlinear boundary dissipation, by transforming it to a Cauchy problem with second order operator differential equations in Hilbert space. Therefore, we transform it, using Green's formula for a triple of Hilbert spaces.
References used
CHUESHOV,I.D, ELLER,M, and LASIECKA,I. ''Finite dimensionality of the attractor for a semi-linear wave equation with non linear boundary dissipation ''. Partial differential equations ,29,No,11-12,1847-1867, 2004
KOPACHEVSKY,N.D, KREIN,S.G, and Nogo Zui Kan. ''Operato methods in linear Hydrodynamics: Evolution and Spectral problems''. Moscow,1989
KOPACHEVSKY,N.D.An abstract Green formula for a triple of Hilbert spaces and its applications to the Stokes problem ,Tavrich. Vestn. Mat. Inf., No. 2, 52–80,2004
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