Reconstruction Robin Boundary Condition in the Heat Conduction Inverse Problem of Fractional Order

2016 ◽  
pp. 147-156 ◽  
Author(s):  
Rafał Brociek ◽  
Damian Słota ◽  
Adam Zielonka
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Fractional Order ◽  
Robin Boundary Condition ◽  
Robin Boundary

Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation

2018 ◽  
Vol 13 (1) ◽  
pp. 5 ◽  
Author(s):  
Rafał Brociek ◽  
Damian Słota
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Fractional Order ◽  
Heat Conduction Equation ◽  
Robin Boundary Condition ◽  
Conduction Equation ◽  
Additional Information ◽  
Bee Colony ◽  
Robin Boundary ◽  
Fractional Heat Conduction

This paper describes an algorithm for reconstruction the boundary condition and order of derivative for the heat conduction equation of fractional order. This fractional order derivative was applied to time variable and was defined as the Caputo derivative. The heat transfer coefficient, occurring in the boundary condition of the third kind, was reconstructed. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem was solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution an Artificial Bee Colony (ABC) algorithm and Nelder-Mead method were used. In order to stabilize the procedure the Tikhonov regularization was applied. The paper presents examples to illustrate the accuracy and stability of the presented algorithm.

Time-fractional heat conduction in an infinite medium with a spherical hole under robin boundary condition

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Linear Combination ◽  
Integral Transforms ◽  
Robin Boundary Condition ◽  
Normal Derivative ◽  
Infinite Medium ◽  
Symmetric Case ◽  
Robin Boundary ◽  
Fractional Heat Conduction

AbstractThe time-fractional heat conduction equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in an infinite medium with a spherical hole in the central symmetric case under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative at the boundary and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary. The integral transforms techniques are used. Several particular cases of the obtained solutions are analyzed. The numerical results are illustrated graphically.

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Linear Combination ◽  
Heat Conduction Equation ◽  
Integral Transform ◽  
Convective Heat Exchange ◽  
Robin Boundary Condition ◽  
Conduction Equation ◽  
Robin Boundary ◽  
Fractional Heat Conduction

AbstractThe central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.

scholarly journals Solutions for parametric double phase Robin problems

2021 ◽  
Vol 121 (2) ◽  
pp. 159-170 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Boundary Condition ◽  
Existence Theorems ◽  
Robin Boundary Condition ◽  
Phase Problem ◽  
Double Phase ◽  
Robin Boundary ◽  
Double Phase Problem

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .

scholarly journals Multiple solutions to a quasilinear Schrödinger equation with Robin boundary condition

2020 ◽  
Vol 5 (4) ◽  
pp. 3825-3839
Author(s):  
Yin Deng ◽  
◽  
Gao Jia ◽  
Fanglan Li ◽  
◽  
...  
Keyword(s):  
Boundary Condition ◽  
Multiple Solutions ◽  
Robin Boundary Condition ◽  
Dinger Equation ◽  
Robin Boundary
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