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Nonlinear Partial Differential Equations for Scientists and Engineers pp 381–423Cite as

Nonlinear Diffusion–Reaction Phenomena

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Abstract

Many physical phenomena are described by the interaction of convection and diffusion and also by the interaction of diffusion and reaction. From a physical point of view, the convection–diffusion process and the diffusion–reaction process are quite fundamental in describing a wide variety of problems in physical, chemical, biological, and engineering sciences. Some nonlinear partial differential equations that model these processes provide many new insights into the question of interaction of nonlinearity and diffusion. It is well known that the Burgers equation is a simple nonlinear model equation representing phenomena described by a balance between convection and diffusion. The Fisher equation is another simple nonlinear model equation which arises in a wide variety of problems involving diffusion and reaction.

The profound study of nature is the most fertile source of mathematical discoveries.

Joseph Fourier

The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty…. It often happens that the requirements of simplicity and beauty are the same, but where they clash the latter must take precedence.

Paul Dirac

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  1. Department of Mathematics, University of Texas, Pan American, 1201 W. University Drive, Edinburg, TX, 78539, USA

    Lokenath Debnath

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Debnath, L. (2012). Nonlinear Diffusion–Reaction Phenomena. In: Nonlinear Partial Differential Equations for Scientists and Engineers. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8265-1_8

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