Manuscript Topics
 

This Special Issue, Mathematical  and Computer Modeling of Nonlinear Phenomena, invites both original and review  manuscripts that bring together novel mathematical concepts and innovative  computational methods that model nonlinear phenomena in real-life. Diffusion  and dispersion processes are crucial in modeling various important phenomena in  life sciences, engineering, and environmental sciences. For example, when  studying spatial patterns and sustained oscillations that biological and  biochemical systems produce or the transport of contaminants in waterbodies or  long wave motion in shallow water one encounters diffusion, dispersion, and  other related processes such as advection, reaction, and sorption. In  population models, various forms of nonlinear diffusion can capture the effects  of crowding or aggregation processes within species. Mathematical models in the  form of time-dependent partial differential equations that have interplay  between diffusion, dispersion, and nonlinear processes can produce fascinating  solutions in the form of traveling waves or target patterns or even solutions  that blow up in finite time. The goal of this Special Issue is to gather  contributions from experts who are working on a variety of interesting  nonlinear models in life sciences, engineering, and environmental sciences. The  contributions can be for models that describe either initial value problems or  initial boundary value problems. Also, time-dependent models can be either  forward in time or backward in time. Innovative computational studies of models  that exploit and corroborate known theoretical results of the models are  welcome. Computational modeling could make use of traditional finite-difference/finite-element  techniques or machine learning approaches such as physics-informed neural  networks.

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