Displaying similar documents to “Inverse Problem for Fractional Diffusion Equation”

On a 3D-Hypersingular Equation of a Problem for a Crack

Samko, Stefan (2011)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 45DB05, 45E05, 78A45 We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.

Exact solutions to some external mixed problems in potential theory

Valery I. Fabrikant (1986)

Aplikace matematiky

Similarity:

A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside....

Short-time heat flow and functions of bounded variation in R N

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We prove a characterisation of sets with finite perimeter and B V functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.

Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

Similarity:

Let R ( λ ) be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that ∫ 1 T | R ( t ) | 2 d t = c T 5 2 + O δ ( T 9 4 + δ ) , where c is a specific nonzero constant and δ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that R ( t ) = O δ ( t 3 4 + δ ) .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the 2 n + 1 -dimensional case. ...