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This work of applied mathematics focuses on the functional study of the nonlinear boundary value problems relating to water flow in porous media, a topic which has up to now gone unexplored in book form. The author shows that abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models, emphasizing the mathematical treatment of their nonlinear aspects.
The volume deals with diffusion type models and emphasizes the mathematical treatment of their nonlinear aspects. The text presents a unifying functional approach to different boundary value problems modelling the water movement in porous media, and the high degree of generality and abstraction is rewarded by the richness of the results obtained in this way.
From the mathematical point of view this research falls under the theory of nonlinear parabolic equations. While water flow in soils is the principal exemplification, the techniques demonstrated and the results obtained are useful for studying other problems in the movement of fluids in porous media, in heat theory, phase transitions, bio
Content Level »Research
Keywords »Boundary value problem - Filtration - Infiltration - Operator - biology - brandonwiskunde - calculus - model - modeling - porous media - soil
Modelling water infiltration in soils.- Brief overview of unsaturated flow concepts.- Settlement of the mathematical models of nonhysteretic infiltration.- Analysis of infiltration models.- Basic existence theorems for evolution equations with monotone operators in Hilbert spaces.- Functional approach to the quasi-unsaturated infiltration model.- Functional approach to the saturated-unsaturated infiltration model.- Specific problems in infiltration.- Inverse problems in infiltration.- Identification of the boundary conditions from recorded observations.- Background tools.