Reaction Diffusion Equations

C. V. Pao
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C. V. Pao: North Carolina State University

Chapter Chapter 1 in Nonlinear Parabolic and Elliptic Equations, 1992, pp 1-46 from Springer

Abstract: Abstract The method of upper and lower solutions and its associated monotone iteration are introduced for both the time-dependent and the steady-state reaction diffusion equations. Based on the principle of conservation a derivation of the equations, including nonlinear boundary conditions, is given in the general framework of reaction diffusion systems. This derivation formulates either a scalar equation or a coupled system of equations, which lead to the underlying subjects to be analyzed in this book. A number of physical models arising from various fields of biological, chemical, and engineering sciences are briefly derived and are used to illuminate the methods. Some examples involving the nonuniqueness problem for the time-dependent equation are included in the discussion.

Keywords: Dirichlet Boundary Condition; Lower Solution; Reaction Function; Reaction Diffusion Equation; Nonlinear Boundary Condition (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-1-4615-3034-3_1

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