The higher-order heat-type equations via signed Lévy stable and generalized Airy functions

We study the higher-order heat-type equation with first time and Mth spatial partial derivatives, M = 2, 3, ... We demonstrate that its exact solutions for M even can be constructed with the help of signed Lévy stable functions. For M odd the same role is played by a special generalization of the Ai...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2013-10, Vol.46 (42), p.425001-16
Main Authors: Górska, K, Horzela, A, Penson, K A, Dattoli, G
Format: Article
Language:English
Subjects:
Airy function
Construction
Derivatives
Evolution
Exact solutions
Functions (mathematics)
generalized Airy function
Initial conditions
Kernels
Mathematical analysis
pseudo-processes
signed Lévy stable functions
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 study the higher-order heat-type equation with first time and Mth spatial partial derivatives, M = 2, 3, ... We demonstrate that its exact solutions for M even can be constructed with the help of signed Lévy stable functions. For M odd the same role is played by a special generalization of the Airy Ai function that we introduce and study. This permits one to generate the exact and explicit heat kernels pertaining to these equations. We examine analytically and graphically the spatial and temporary evolution of particular solutions for simple initial conditions.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/42/425001