Analysis of stochastic groundwater problems. Part I: Deterministic partial differential equations in groundwater flow. A functional-analytic approach

Abstract

Functional-analytic theory is introduced as a method to analyse the problem of deterministic partial differential equations of the type appearing in groundwater flow. Equations are treated as abstract evolution equations for elliptic partial differential operators in an appropriate functional Sobolev space, for which a strongly continuous semigroup exists. A semigroup solution is then developed and its application to regional groundwater flow is indicated. The theoretical framework presented in Part I serves as introduction for the stochastic groundwater flow problem presented in Part II and gives an unified conception of the deterministic and the stochastic problem.