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Entire Solutions for Bistable Lattice Differential Equations with Obstacles

Aaron Hoffman
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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.
      Format: Paperback / softback CONTRIBUTORS: Aaron Hoffman EAN: 9781470422011 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-11-01 CITY: GENRE: MATHEMATICS / Differential Equations / General WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations

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      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.
      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.
      Format: Paperback / softback CONTRIBUTORS: Aaron Hoffman EAN: 9781470422011 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2017-11-01 CITY: GENRE: MATHEMATICS / Differential Equations / General WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations

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      Be the first to write a review
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      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.

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