An inverse time-fractional diffusion problem with Robin boundary condition in two layers spherical domain

2021 ◽  
Vol 40 (8) ◽  
Author(s):  
Tran Nhat Luan
Keyword(s):  
Boundary Condition ◽  
Robin Boundary Condition ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Spherical Domain ◽  
Robin Boundary

scholarly journals Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Jukka Kemppainen
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Diffusion Equation ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Robin Boundary Condition ◽  
Fractional Diffusion ◽  
Uniqueness Of The Solution ◽  
Time Fractional Diffusion Equation ◽  
Robin Boundary

Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition on a bounded domain with Lyapunov boundary is proved in the space of continuous functions up to boundary. Since a Green matrix of the problem is known, we may seek the solution as the linear combination of the single-layer potential, the volume potential, and the Poisson integral. Then the original problem may be reduced to a Volterra integral equation of the second kind associated with a compact operator. Classical analysis may be employed to show that the corresponding integral equation has a unique solution if the boundary data is continuous, the initial data is continuously differentiable, and the source term is Hölder continuous in the spatial variable. This in turn proves that the original problem has a unique solution.

Fractional diffusion equation in half-space with Robin boundary condition

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Jun-Sheng Duan ◽  
Zhong Wang ◽  
Shou-Zhong Fu
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Half Space ◽  
Boundary Value ◽  
Robin Boundary Condition ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Initial Value ◽  
Robin Boundary

AbstractThe initial and boundary value problem for the fractional diffusion equation in half-space with the Robin boundary condition is considered. The solution is comprised of two parts: the contribution of the initial value and the contribution of the boundary value, for which the respective fundamental solutions are given. Finally, the solution formula of the considered problem is obtained.

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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