β Scribed by B. H. Gilding
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The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The emphasis is on the interpretation of the results of the analysis. These are explained in terms of the qualitative behaviour of the flow of water in an unsaturated soil which is described by the Richards equation.
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Dordan, O., Mathematical problems arising in qualitative simulation of a differential equation, Artificial Intelligence 55 (1992) 61-86. Kuiper's QSIM algorithm is an expert system which studies the qualitative evolution of a differential inclusion. This paper addresses several issues raised by QSI
We study the Cauchy problem of multidimensional viscous diffusion equations. By using an equivalent integral equation, we first give the existence of local solutions. Then, under some assumptions, we obtain the global existence of solutions.