Entire Solutions for Bistable Lattice Differential Equations with Obstacles.

Entire Solutions for Bistable Lattice Differential Equations with Obstacles.

The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice. Their work generalizes to the discret...

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Bibliographic Details
Main Author: Hoffman, Aaron
Other Authors: Hupkes, Hermen, Vleck, E. S. Van
Format: eBook
Language:English
Published: Providence : American Mathematical Society, 2018.
Series:Memoirs of the American Mathematical Society.
Subjects:
Lattice theory.
Differential equations.
Differential equations
Lattice theory
Online Access:Click for online access
Table of Contents:
  • Cover; Title page; Chapter 1. Introduction; Reaction-Diffusion Problems; Existence of Waves; Stability of Waves; The Program; Pre-interaction regime; Interaction regime; Post-interaction regime
  • rest state; Post-interaction regime
  • convergence to wave; Organization; Chapter 2. Main Results; 2.1. Homogeneous Lattice; 2.2. Obstructed Lattice; Chapter 3. Preliminaries; Chapter 4. Spreading Speed; Chapter 5. Large Disturbances; 5.1. Notation; 5.2. Preliminary Computations; 5.3. The Ansatz; 5.4. The expanding plateau; 5.5. The function; 5.6. Construction of sub-solution.
  • Chapter 6. The Entire SolutionChapter 7. Various Limits; Chapter 8. Proof of Theorem 2.3; Chapter 9. Discussion; Acknowledgments; Bibliography; Back Cover.

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