FUNDAMENTAL SOLUTION OF HEAT EQUATION IN CONDENSED PHASE

2018 ◽  
Vol 100 (2) ◽  
pp. 167-180
Author(s):  
E. V. Alves ◽  
M. J. Alves
Keyword(s):  
Fundamental Solution ◽  
Heat Equation ◽  
Condensed Phase

scholarly journals Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues

2018 ◽  
Vol 50 (2) ◽  
pp. 373-395 ◽  
Author(s):  
Dmitri Finkelshtein ◽  
Pasha Tkachov
Keyword(s):  
Fundamental Solution ◽  
Heat Equation ◽  
Probability Density ◽  
Real Line ◽  
The Real ◽  
Probability Densities ◽  
Tail Asymptotic

Abstract We study the tail asymptotic of subexponential probability densities on the real line. Namely, we show that the n-fold convolution of a subexponential probability density on the real line is asymptotically equivalent to this density multiplied by n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular subexponential functions and use it to find an analogue of Kesten's bound for functions on ℝd. The results are applied to the study of the fundamental solution to a nonlocal heat equation.

Asymptotic behaviour of the fundamental solution to ∂ u /∂ t = — ( — ∆) m u

1993 ◽  
Vol 441 (1912) ◽  
pp. 423-432 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Positive Integer ◽  
Fundamental Solution ◽  
Heat Equation ◽  
Asymptotic Behaviour ◽  
Infinite Number ◽  
Fourier Integral ◽  
Number Of Zeros

An asymptotic expansion is derived for the Fourier integral f ^ ( x ) = 1 ( 2 π ) n / 2 ∫ R n exp ( − | q | 2 m + i x ⋅ q ) d q , x ε R n as | x | →∞, where m is a positive integer. From this, it is deduced that the fundamental solution to the ‘heat’ equation ∂ u / ∂ t = − ( − Δ ) m u has an infinite number of zeros tending to infinity.

scholarly journals The inversion of a transform related to the Laplace transform and to heat conduction

1964 ◽  
Vol 4 (1) ◽  
pp. 1-14 ◽  
Author(s):  
David V. Widder
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Heat Equation ◽  
Laplace Transform ◽  
Physical Interpretation ◽  
Integral Transform ◽  
The Laplace Transform ◽  
Image Position

In a recent paper [7] the author considered, among other things, the integral transform where is the fundamental solution of the heat equation There we gave a physical interpretation of the transform (1.1). Here we shall choose a slightly different interpretation, more convenient for our present purposes. If then u(O, t) = f(t). That is, the function f(t) defined by equation (1.1) is the temperature at the origin (x = 0) of an infinite bar along the x-axis t seconds after it was at a temperature defined by the equation .

scholarly journals Conformable heat equation on a radial symmetric plate

2017 ◽  
Vol 21 (2) ◽  
pp. 819-826 ◽  
Author(s):  
Derya Avci ◽  
Eroglu Iskender ◽  
Necati Ozdemir
Keyword(s):  
Fundamental Solution ◽  
Heat Equation ◽  
Analytical Method ◽  
Numerical Scheme ◽  
Fractional Derivatives ◽  
Problem Formulation ◽  
Computational Results ◽  
Conformable Derivative ◽  
Local Structures ◽  
Non Local

The conformable heat equation is defined in terms of a local and limit-based definition called conformable derivative which provides some basic properties of integer order derivative such that conventional fractional derivatives lose some of them due to their non-local structures. In this paper, we aim to find the fundamental solution of a conformable heat equation acting on a radial symmetric plate. Moreover, we give a comparison between the new conformable and the existing Grunwald-Letnikov solutions of heat equation. The computational results show that conformable formulation is quite successful to show the sub-behaviors of heat process. In addition, conformable solution can be obtained by a analytical method without the need of a numerical scheme and any restrictions on the problem formulation. This is surely a significant advantageous compared to the Grunwald-Letnikov solution.

scholarly journals On fractional heat equation

2021 ◽  
Vol 24 (1) ◽  
pp. 73-87
Author(s):  
Anatoly N. Kochubei ◽  
Yuri Kondratiev ◽  
José Luís da Silva
Keyword(s):  
Brownian Motion ◽  
Fundamental Solution ◽  
Heat Equation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Convolution Operators ◽  
Fractional Heat Equation ◽  
Long Time ◽  
Time Changes ◽  
Distributed Order

Abstract In this paper, the long-time behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the Caputo-Djrbashian fractional derivative and more general cases corresponding to differential-convolution operators, in particular, distributed order derivatives.

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