FUNCTIONAL APPROACH TO NONLINEAR MODELS OF WATER FLOW IN SOILS
CONTENTS PART I MODELLING WATER IN?LTRATION IN SOILS BRIEF OVERVIEW OF UNSATURATED ?OW CONCEPTS SOME BASIC DE?NITIONS IN THE UNSATURATED ?OW RICHARDS’ EQUATION PRESENTATION OF THE EMPIRICAL HYDRAULIC MODELS COMMENTS SETTLEMENT OF THE MATHEMATICAL MODELS OF NONHYSTERETIC IN?LTRATION PHYSICAL CONTEXT AND MATHEMATICAL HYPOTHESES STRONGLY NONLINEAR SATURATED-UNSATURATED DI?USIVE MODEL WEAKLY NONLINEAR SATURATED-UNSATURATED DI?USIVE MODEL QUASI-UNSATURATED MODEL DEGENERATE MODELS EXTENSIONS OF THE FUNCTIONS BELOW THE ?ELD CAPACITY DIMENSIONLESS FORM OF THE DI?USIVE MODELS PART II ANALYSIS OF IN?LTRATION MODELS BASIC EXISTENCE THEOREMS FOR EVOLUTION EQUATIONS THE SEMIGROUP APPROACH NONLINEAR M-ACCRETIVE OPERATORS IN HILBERT SPACES THE CAUCHY PROBLEM WITHIN THE SEMIGROUP APPROACH THE CAUCHY PROBLEM WITHIN THE VARIATIONAL APPROACH FUNCTIONAL APPROACH TO THE QUASI-UNSATURATED IN?LTRATION MODEL BASIC HYPOTHESES FOR THE QUASI-UNSATURATED MODEL PRELIMINARY RESULTS STRONGLY NONLINEAR CONDUCTIVITY HOMOGENEOUS DIRICHLET WEAKLY NONLINEAR CONDUCTIVITY NONHOMOGENEOUS DIRICHLET FUNCTIONAL APPROACH TO THE SATURATED-UNSATURATED IN?LTRATION MODEL BASIC HYPOTHESES FOR THE SATURATED-UNSATURATED MODEL THE APPROXIMATING PROBLEM THE ORIGINAL PROBLEM THE WEAK SOLUTION IN THE PRESSURE FORM EXISTENCE OF THE FREE BOUNDARY UNIQUENESS OF THE WEAK SOLUTION SPECI?C PROBLEMS IN IN?LTRATION ANALYSIS OF THE DI?USIVITY-DEGENERATE MODEL ANALYSIS OF THE POROSITY-DEGENERATE MODEL ANALYSIS OF AN IN?LTRATION HYSTERETIC MODEL PART III INVERSE PROBLEMS IN IN?LTRATION IDENTI?CATION OF THE BOUNDARY CONDITIONS FROM RECORDED OBSERVATIONS BASIC CONCEPTS IN THE THEORY OF OPTIMAL CONTROL THE IDENTI?CATION PROBLEM SETTLEMENT IDENTI?CATION USING TIME AVERAGE OBSERVATIONS CASE OF A PLANE SOIL SURFACE IDENTI?CATION PROBLEM USING ?NAL TIME OBSERVATIONS BOUNDARY CONDITIONS BOUNDARY CONDITIONS BOUNDARY CONDITIONS A BACKGROUND TOOLS A 1 SOME DE?NITIONS AND RESULTS IN BANACH SPACES A 2 LP SPACES AND SOBOLEV SPACES A 3 VECTORIAL DISTRIBUTIONS AND W K,P SPACES A 4 OPERATORS IN BANACH SPACES A 5 CONVEX FUNCTIONS AND SUBDI?ERENTIAL MAPPINGS A 6 VARIOUS FORMULAS REFERENCES