Abstract
In various areas of physics and chemistry a number of processes can be described by nonlinear diffusion equations. A special class of these systems is given by a linear partial differential equation with nonlinear boundary conditions. The most well-known example is a heating process by radiation which is described on the boundary by the “Stefan-Boltzmann law” or “fourth-power law”. Another example is heat transfer by convection which results not in an exponent of order 4 but 5/4. Both processes are described by Carslaw/Jaeger [2],§ 19, for example. In chemical reactions Ross[9] gives a process where the boundary condition is ruled by the “Michaelis-Menten law”.
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Sachs, E. (1978). Optimal Control for a Class of Integral Equations. In: Henn, R., Korte, B., Oettli, W. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95322-4_23
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DOI: https://doi.org/10.1007/978-3-642-95322-4_23
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