On the Poincaré theorem with asymptotically periodic coefficients

1998 ◽  
Vol 50 (9) ◽  
pp. 1442-1448
Author(s):  
S. F. Buslaeva
Keyword(s):  
Periodic Coefficients ◽  
Asymptotically Periodic ◽  
Poincare Theorem

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

Homogenization of the parabolic equation with periodic coefficients at the edge of a spectral gap

2021 ◽  
pp. 1-33
Author(s):  
A. R. Akhmatova ◽  
E. S. Aksenova ◽  
V. A. Sloushch ◽  
T. A. Suslina
Keyword(s):  
Parabolic Equation ◽  
Spectral Gap ◽  
Periodic Coefficients
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