General Solutions of the Heat Equation

2011 ◽  
pp. 111-126 ◽  
Author(s):  
Dieter Bäuerle
Keyword(s):  
Heat Equation ◽  
General Solutions

General solutions of the heat equation

2020 ◽  
Vol 539 ◽  
pp. 122914
Author(s):  
ByoungSeon Choi ◽  
Chansoo Kim ◽  
Hyuk Kang ◽  
M.Y. Choi
Keyword(s):  
Heat Equation ◽  
General Solutions

scholarly journals Generalized special functions in the description of fractional diffusive equations

2019 ◽  
Vol 10 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Clemente Cesarano
Keyword(s):  
Heat Equation ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Special Functions ◽  
Hermite Polynomials ◽  
Generalized Equations ◽  
Extended Form ◽  
General Solutions

Abstract Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.

SPECTRAL PROBLEMS ARISING IN THE STABILIZATION PROBLEM FOR THE LOADED HEAT EQUATION: A TWO-DIMENSIONAL AND MULTI-POINT CASES

2019 ◽  
Vol 7 (1) ◽  
pp. 23-37
Author(s):  
Jenaliyev M.T. ◽  
◽  
Imanberdiyev K.B. ◽  
Kassymbekova A.S. ◽  
Sharipov K.S. ◽  
...  
Keyword(s):  
Heat Equation ◽  
Two Dimensional ◽  
Stabilization Problem ◽  
Spectral Problems
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