scholarly journals An inverse radiative coefficient problem arising in a two-dimensional heat conduction equation with a homogeneous Dirichlet boundary condition in a circular section

2016 ◽  
Vol 435 (1) ◽  
pp. 917-943 ◽  
Author(s):  
Liu Yang ◽  
Zui-Cha Deng
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Dirichlet Boundary Condition ◽  
Heat Conduction Equation ◽  
Dirichlet Boundary ◽  
Conduction Equation ◽  
Two Dimensional ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Coefficient Problem ◽  
Circular Section

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.

scholarly journals A Lotka-Volterra Competition Model with Cross-Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenyan Chen ◽  
Ya Chen
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Cross Diffusion ◽  
Existence Of Positive Solutions

A Lotka-Volterra competition model with cross-diffusions under homogeneous Dirichlet boundary condition is considered, where cross-diffusions are included in such a way that the two species run away from each other because of the competition between them. Using the method of upper and lower solutions, sufficient conditions for the existence of positive solutions are provided when the cross-diffusions are sufficiently small. Furthermore, the investigation of nonexistence of positive solutions is also presented.

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