scholarly journals The existence of a global fundamental solution for homogeneous Hörmander operators via a global lifting method

2017 ◽  
Vol 114 (5) ◽  
pp. 855-889 ◽  
Author(s):  
Stefano Biagi ◽  
Andrea Bonfiglioli
Keyword(s):  
Fundamental Solution ◽  
Hörmander Operators

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

A study of plane wave and fundamental solution in the theory of microstretch thermoelastic diffusion solid with phase-lag models

2015 ◽  
Vol 11 (2) ◽  
pp. 160-185 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sanjeev Ahuja ◽  
S.K. Garg
Keyword(s):  
Fundamental Solution ◽  
Plane Wave ◽  
Phase Lag ◽  
Dual Phase ◽  
Elementary Functions ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Propagation Technique ◽  
Steady Oscillations ◽  
Phase Velocity And Attenuation

Purpose – The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions. Design/methodology/approach – Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem. Findings – Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived. Originality/value – Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

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