Existence and uniqueness of the solution of a differential equation of fractional diffusion
Author(s):
Alexander Fedorovich Tedeev
PhD in phisics and mathematics
Assoc.Professor
Dept. of functional analysis and differential equations
K. Khetagurov North-Osetian State University
Vatutin str. 44-46,
362025, Vladikaukaz, RSO-A, Russia
tedeev92@bk.ru
Abstract:
In this paper we consider a mixed Dirichlet
problem for a linear homogeneous fractional diffusion equation. The
existence and uniqueness of the solution of the problem using the
harmonic continuation of the solution is proved. As a result, the
solution of the differential equation is defined as a trace of a
harmonic function. This approach allows us
to introduce an integral identity whose solutions are pairs of functions such that
the first coordinate of this pair is the desired solution, and the second one
is its harmonic continuation. The continuity of the first
coordinate in the integral norm is proved as well.
Keywords
- a pair of functions
- fractional diffusion
- mixed Dirichlet problem
- weak solution
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