51 resultados para Partial Differential Equation
em Bulgarian Digital Mathematics Library at IMI-BAS
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2000 Mathematics Subject Classification: 60H15, 60H40
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An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.
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Mathematics Subject Classification: 26A33, 76M35, 82B31
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Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.
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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.
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2000 Mathematics Subject Classification: 42B10, 43A32.
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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05
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2000 Mathematics Subject Classification: 34K15, 34C10.
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Кремена В. Стефанова - В тази статия са разрешени някои нелинейни интегрални неравенства, които включват максимума на неизвестната функция на две променливи. Разгледаните неравенства представляват обобщения на класическото неравенство на Гронуол-Белман. Значението на тези интегрални неравенства се определя от широките им приложения в качествените изследвания на частните диференциални уравнения с “максимуми” и е илюстрирано чрез някои директни приложения.
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2002 Mathematics Subject Classification: 35S05
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2002 Mathematics Subject Classification: 35S05
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* This work has been supported by the Office of Naval Research Contract Nr. N0014-91-J1343, the Army Research Office Contract Nr. DAAD 19-02-1-0028, the National Science Foundation grants DMS-0221642 and DMS-0200665, the Deutsche Forschungsgemeinschaft grant SFB 401, the IHP Network “Breaking Complexity” funded by the European Commission and the Alexan- der von Humboldt Foundation.