Entire Solutions for Bistable Lattice Differential Equations with Obstacles
Aaron Hoffman · Hermen Hupke · E. S. Van Vleck
Jan 2018 · American Mathematical Soc.
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Ebook
119
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About this ebook
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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3.8
10 reviews
Toppi Notowidjoyo
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February 11, 2021
The language style is too technical or maybe bit complecated
sam sung
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November 28, 2020
ttttbi
1 person found this review helpful
About the author
Aaron Hoffman: Franklin W. Olin College of Engineering, Needham, MA, USA,
Hermen Hupkes: Mathematisch Instituut, Universiteit Leiden, Leiden, The Netherlands,
E. S. Van Vleck: University of Kansas, Lawrence, KS, USA
Hermen Hupkes: Mathematisch Instituut, Universiteit Leiden, Leiden, The Netherlands,
E. S. Van Vleck: University of Kansas, Lawrence, KS, USA
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