Entire Solutions for Bistable Lattice Differential Equations with Obstacles

Aaron Hoffman, Hermen Hupkes, E.S. Van Vleck (Autoren)

Buch | Softcover

117 Seiten

2018
American Mathematical Society (Verlag)
978-1-4704-2201-1 (ISBN)

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Considers 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.

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 discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.

Aaron Hoffman, Franklin W. Olin College of Engineering, Needham, MA. Hermen Hupkes, Mathematisch Instituut, Universiteit Leiden, The Netherlands. E.S. Van Vleck, University of Kansas, Lawrence, KS.

Introduction
Main results
Preliminaries
Spreading speed
Large disturbances
The entire solution
Various limits
Proof of Theorem 2.3
Discussion
Acknowledgments
Bibliography.

Erscheinungsdatum	05.11.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	255 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-2201-8 / 1470422018
ISBN-13	978-1-4704-2201-1 / 9781470422011
Zustand	Neuware