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- W2053707930 abstract "A one-dimensional quasilinear autonomous parabolic equation is being considered; it generalizes a well-known equation which occurs, for example, in the theory of radiation heat conduction and diffusion in porous media. The “diffusion” coefficient is of the power law type in the dependent and in the independent space variable. An additive “drift” term is admitted which is linear in the dependent variable and depends in general on the independent space variable. The basic equation has a conservative linear-similarity solution (except possibly on a set of measure zero) which may be interpreted as a nonlinear distribution process from a completely concentrated initial state. For each fixed positive time value, this solution vanishes outside a (bounded) support interval of the space variable. Under appropriate conditions on the parameters contained in the equation there exists even a conservative linear-similarity solution which tends to a steady state as time increases indefinitely. The nonlinear distribution process is a generalization of a corresponding linear one which is determined by the (linear) generalized Feller equation. The nonlinear equation considered here goes over in the limit, as the nonlinearity parameter goes to zero, into the generalized Feller equation. Of particular interest are the distribution laws of Maxwell, Wien, and Gauss (which are special cases of the generalized Feller distribution law) and their nonlinear generalizations." @default.
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- W2053707930 date "1978-12-01" @default.
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- W2053707930 title "Conservative Solutions of One-Dimensional Nonlinear Distribution Processes with Drift" @default.
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- W2053707930 doi "https://doi.org/10.1137/0135064" @default.
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