Preface: Special issue on dissipativesystems and applications with emphasis on nonlocal or nonlinear diffusion problems

Georg Hetzer; Wenxian Shen

doi:10.3934/dcds.2015.35.4i

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2015, Volume 35, Issue 4: i-iii. Doi: 10.3934/dcds.2015.35.4i open access

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Preface: Special issue on dissipative systems and applications with emphasis on nonlocal or nonlinear diffusion problems

Georg Hetzer^1, and
Wenxian Shen^2,

1.
Mathematics & Statistics, Auburn University, College of Sciences and Mathematics, 221 Parker, Auburn, Alabama 36849
2.
Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849

Published: May 2017

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The strong interest in infinite dimensional dissipative systems originated from the observation that the dynamics of large classes of partial differential equations and systems resembles the behavior known from the modern theory of finite-dimensional dynamical systems. Reaction-diffusion problems are typical examples in this context. In biological applications linear diffusion represents random dispersal of a species, but in many cases other dispersal strategies occur, which has led to models with cross diffusion and nonlocal dispersal.

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