971 resultados para Partial Differential Equation
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"Only the material on elliptic equations will appear in these notes."
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Mimeographed.
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Bibliography: p. 165-170.
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Originally presented as the author's thesis, University of Illinois at Urbana-Champaign.
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Supported in part by National Science Foundation under Grant No. U.S. NSF-GJ-328.
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Includes bibliographical references (20).
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Vita.
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Cover title.
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Bibliography: leaf [77]
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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006
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We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.
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In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).
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The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.