scholarly journals Symmetry and explicit solutions of partial differential equations

1992 ◽  
Vol 10 (3-4) ◽  
pp. 307-324 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Explicit Solutions ◽  
Partial Differential

scholarly journals Explicit solutions for partial differential equations of Lord-Shulman thermoelasticity

2009 ◽  
Vol 36 (2) ◽  
pp. 137-156
Author(s):  
A. Rodionov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Explicit Solutions ◽  
Partial Differential ◽  
Relaxation Constant ◽  
Linear Partial Differential Equations ◽  
Finite Sums

We consider the Lord-Shulman model of thermoelasticity with one relaxation constant. The corresponding system of four linear partial differential equations is solved by means of holomorphic expansions. We prove the convergence of expansions and study the possibility to convert them in finite sums.

scholarly journals Explicit solutions of some fractional partial differential equations via stable subordinators

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Latifa Debbi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fundamental Solutions ◽  
Explicit Solutions ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Stable Law ◽  
One Dimensional ◽  
Fractional Equations ◽  
Canonical Processes

The aim of this work is to represent the solutions of one-dimensional fractional partial differential equations (FPDEs) of order (α∈ℝ+\ℕ) in both quasi-probabilistic and probabilistic ways. The canonical processes used are generalizations of stable Lévy processes. The fundamental solutions of the fractional equations are given as functionals of stable subordinators. The functions used generalize the functions given by the Airy integral of Sirovich (1971). As a consequence of this representation, an explicit form is given to the density of the 3/2-stable law and to the density of escaping island vicinity in vortex medium. Other connected FPDEs are also considered.

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