Cauchy problem for fractional diffusion-wave equations with variable coefficients

We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial variables. This equation describes the propagation of stress pulses in a visco...

Full description

Saved in:
Bibliographic Details
Published in:Applicable analysis 2014-10, Vol.93 (10), p.2211-2242
Main Author: Kochubei, Anatoly N.
Format: Article
Language:English
Subjects:
Caputo-Dzhrbashyan fractional derivative
Cauchy problem
Cauchy problems
Construction
Derivatives
Diffusion
Evolution
fractional diffusion-wave equation
Fractions
fundamental solution of the Cauchy problem
Mathematical analysis
Operators
Primary: 35R11
Propagation
Secondary: 35K70
Theorems
Uniqueness theorems
Variables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial variables. This equation describes the propagation of stress pulses in a viscoelastic medium. Its properties are intermediate between those of parabolic and hyperbolic equations. In this paper, we construct and investigate a fundamental solution of the Cauchy problem, prove existence and uniqueness theorems for such equations.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2013.875162