Displaying similar documents to “Towards the Cauchy problem for the Laplace equation”

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

Kilbas, Anatoly, Trujillo, Juan, Voroshilov, Aleksandr (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 35A15, 44A15, 26A33 The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.

Cauchy Problem for Differential Equation with Caputo Derivative

Kilbas, Anatoly, Marzan, Sergei (2004)

Fractional Calculus and Applied Analysis

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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...

The Fuchsian Cauchy problem.

Belarbi, Malika, Mechab, Mustapha (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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On the Cauchy problem in a class of entire functions in several variables

Eugeni Leinartas (1996)

Banach Center Publications

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We study the integral representation of solutions to the Cauchy problem for a differential equation with constant coefficients. The Cauchy data and the right-hand of the equation are given by entire functions on a complex hyperplane of n + 1 . The Borel transformation of power series and residue theory are used as the main methods of investigation.

L p - L q -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

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We prove the L p - L q -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the L p - L q -time decay estimates.