scholarly journals Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

2018 ◽  
Vol 37 (4) ◽  
pp. 4475-4483 ◽  
Author(s):  
Yuriy Povstenko ◽  
Joanna Klekot
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Heat Absorption ◽  
Fractional Heat Conduction

scholarly journals A note on the integral approach to non-linear heat conduction with Jeffrey’s fading memory

2013 ◽  
Vol 17 (3) ◽  
pp. 733-737 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Boundary Condition ◽  
Approximate Solution ◽  
Heat Conduction ◽  
Dirichlet Boundary Condition ◽  
Heat Conduction Equation ◽  
Dirichlet Boundary ◽  
Integral Approach ◽  
Fading Memory ◽  
Fourier Law ◽  
Viscous Effects

Integral approach by using approximate profile is successfully applied to heat conduction equation with fading memory expressed by a Jeffrey?s kernel. The solution is straightforward and the final form of the approximate temperature profile clearly delineates the ?viscous effects? corresponding to the classical Fourier law and the relaxation (fading memory). The optimal exponent of the approximate solution is discussed in case of Dirichlet boundary condition.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

On the Dispersive Estimate for the Dirichlet Schrödinger Propagator and Applications to Energy Critical NLS

2014 ◽  
Vol 66 (5) ◽  
pp. 1110-1142
Author(s):  
Dong Li ◽  
Guixiang Xu ◽  
Xiaoyi Zhang
Keyword(s):  
Boundary Condition ◽  
Fundamental Solution ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Obstacle Problem ◽  
Dirichlet Boundary ◽  
Radial Symmetry ◽  
Well Posedness ◽  
Robust Algorithm ◽  
Dispersive Estimate

AbstractWe consider the obstacle problem for the Schrödinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrödinger propagator and give a robust algorithm to prove sharp L1 → L∞ dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well–posedness and scattering for defocusing energy-critical NLS on with Dirichlet boundary condition and radial data in these dimensions.

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