Entire Solutions for Bistable Lattice Differential Equations with Obstacles (häftad)
Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
117
Utgivningsdatum
2017-11-01
Förlag
American Mathematical Society
ISBN
9781470422011
Entire Solutions for Bistable Lattice Differential Equations with Obstacles (häftad)

Entire Solutions for Bistable Lattice Differential Equations with Obstacles

Häftad Engelska, 2017-11-01
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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.
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Övrig information

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.

Innehållsförteckning

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