Fundamental solution in the linear theory of thermoviscoelastic mixtures

2007 ◽  
Vol 18 (3) ◽  
pp. 323-335 ◽  
Author(s):  
MERAB SVANADZE ◽  
GERARDO IOVANE
Keyword(s):  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Linear Theory ◽  
Elementary Functions ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Basic Properties ◽  
Steady Vibrations ◽  
Steady Oscillations

In this article the linear theory of thermoviscoelastic mixtures is considered. The fundamental solution of the system of linear-coupled partial differential equations of steady oscillations (steady vibrations) of the theory of thermoviscoelastic mixtures is constructed in terms of elementary functions and basic properties are established.

Fundamental solution of the system of equations of pseudo oscillations in the theory of thermoelastic diffusion materials with double porosity

2019 ◽  
Vol 15 (2) ◽  
pp. 317-336 ◽  
Author(s):  
Tarun Kansal
Keyword(s):  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Volume Fraction ◽  
Displacement Vector ◽  
Double Porosity ◽  
Elementary Functions ◽  
Partial Differential ◽  
Thermoelastic Diffusion ◽  
Content Type

PurposeThe purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity.Design/methodology/approachThe paper deals with the study of pseudo oscillations in the generalized theory of thermoelastic diffusion materials with double porosity.FindingsThe paper finds the fundamental solution of partial differential equations in terms of elementary functions.Originality/valueAssuming the displacement vector, volume fraction fields, temperature change and chemical potential functions in terms of oscillation frequency in the governing equations, pseudo oscillations have been studied and finally the fundamental solution of partial differential equations in case of pseudo oscillations in terms of elementary functions has been constructed.

scholarly journals Fundamental Solution in Micropolar Viscothermoelastic Solids with Void

2015 ◽  
Vol 20 (1) ◽  
pp. 109-125 ◽  
Author(s):  
R. Kumar ◽  
K.D. Sharma ◽  
S.K. Garg
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Present Article ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Basic Properties ◽  
Steady Oscillations

Abstract In the present article, we construct the fundamental solution to a system of differential equations in micropolar viscothermoelastic solids with voids in case of steady oscillations in terms of elementary functions. Some basic properties of the fundamental solution are also established.

scholarly journals Fundamental Solution in the Theory of Thermomicrostretch Elastic Diffusive Solids

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Basic Properties ◽  
Special Cases ◽  
Steady Oscillations

We construct the fundamental solution of system of differential equations in the theory of thermomicrostretch elastic diffusive solids in case of steady oscillations in terms of elementary functions. Some basic properties of the fundamental solution are established. Some special cases are also discussed.

Fundamental Solution via Invariant Approach for a Brain Tumor Model and its Extensions

2014 ◽  
Vol 69 (12) ◽  
pp. 725-732 ◽  
Author(s):  
Andrew G. Johnpillai ◽  
Fazal M. Mahomed ◽  
Saeid Abbasbandy
Keyword(s):  
Brain Tumor ◽  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tumor Models ◽  
Partial Differential ◽  
Equivalence Transformations ◽  
Extended Class

AbstractWe firstly show how one can use the invariant criteria for a scalar linear (1+1) parabolic partial differential equations to perform reduction under equivalence transformations to the first Lie canonical form for a class of brain tumor models. Fundamental solution for the underlying class of models via these transformations is thereby found by making use of the well-known fundamental solution of the classical heat equation. The closed-form solution of the Cauchy initial value problem of the model equations is then obtained as well. We also demonstrate the utility of the invariant method for the extended form of the class of brain tumor models and find in a simple and elegant way the possible forms of the arbitrary functions appearing in the extended class of partial differential equations. We also derive the equivalence transformations which completely classify the underlying extended class of partial differential equations into the Lie canonical forms. Examples are provided as illustration of the results.

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