广义函数法边界积分方程的建立
The Establishment of Boundary Integral Equations by Generalized Functions
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摘要: 从广义函数论出发,本文引入一特殊广义函数δθP,通过它以及它的各阶导数建立了任一足够光滑函数的各阶导数的边界积分方程。对于由线性偏微分算子定义的问题,只要存在着相应的基本解,问题的偏微分方程总可转换成边界积分方程。Abstract: By the theory of generalized functions this paper introduces a specific generalized function δθP, by which, together with its various derivatives, the boundary integral equations and its arbitrary derivatives of any sufficiently smooth function can be established. These equations have no non-integral singularities. For a problem defined by linear partial differential operators, the partial differential equations of the problem can always be converted into boundary integral equations so long as the relevant fundamental solutions exist.
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[1] Love,A.E.H.,A Treatise on the Mathematical Theory of Elasticity, 4th edition, Dover, New York (1944). [2] Pearson, C. E., Theoretical Elasticty (1959). [3] Villaggio, P., Qualitative Methods in Elasticity(1977). [4] Fredholm, J., Solution d'un Probleme fondamental de.la Theorie de I'Elasticite, Arch. Mat.Astronomi och Fysik, 2 (1906),1-8. [5] Kellogg, O. D, Foundations of Potential Theory(1953). [6] Sternberg, W. J. and T. L. Smith, The Theory of Potential and Spherical Harmonics (1944). [7] Muskhelishvili, N. I., Singular Integral Equations (1953). [8] Mikhlin, S.G,Integral Equations(1957). [9] Gel'fand, I.and G.Silov,Generalized Functions,1-4 (1964). [10] Flanders,H.,Differential Forms(1963). -
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