On the Laplace equation with a supercritical nonlinear Robin boundary condition in the half-space

2012 ◽  
Vol 47 (3-4) ◽  
pp. 667-682 ◽  
Author(s):  
Lucas C. F. Ferreira ◽  
Everaldo S. Medeiros ◽  
Marcelo Montenegro
Keyword(s):  
Boundary Condition ◽  
Half Space ◽  
Laplace Equation ◽  
Robin Boundary Condition ◽  
Robin Boundary

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 + .

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