An Improved Linearity-Preserving Cell-Centered Scheme for Nonlinear Diffusion Problems on General Meshes

2021 ◽  
Vol 14 (2) ◽  
pp. 405-437
Author(s):  
Cheng Dong & Tong Kang
Keyword(s):  
Nonlinear Diffusion ◽  
General Meshes ◽  
Diffusion Problems

scholarly journals Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Shrödinger Equation with Complicated Potential

2021 ◽  
Author(s):  
Michael I. Tribelsky
Keyword(s):  
Ground State ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Dinger Equation ◽  
Bottom Part ◽  
Diffusion Type ◽  
Traveling Pulses ◽  
General Method ◽  
Diffusion Problems

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

scholarly journals Approximate solutions to a new class of nonlinear diffusion problems

1999 ◽  
Vol 108 (1-2) ◽  
pp. 219-231 ◽  
Author(s):  
Alberto Cabada ◽  
Juan J. Nieto ◽  
Rodrigo L. Pouso
Keyword(s):  
Nonlinear Diffusion ◽  
Approximate Solutions ◽  
New Class ◽  
Diffusion Problems

scholarly journals Stability of solutions of nonlinear diffusion problems

1966 ◽  
Vol 14 (2) ◽  
pp. 221-241 ◽  
Author(s):  
Leonard D Peterson ◽  
Clair G Maple
Keyword(s):  
Nonlinear Diffusion ◽  
Stability Of Solutions ◽  
Diffusion Problems

scholarly journals Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Shrödinger Equation with Complicated Potential

2021 ◽  
Author(s):  
Michael I. Tribelsky
Keyword(s):  
Ground State ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Bottom Part ◽  
Diffusion Type ◽  
Traveling Pulses ◽  
General Method ◽  
Diffusion Problems ◽  
Shrodinger Equation

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

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