By Charles Hayes
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Additional info for Concepts of real analysis
For example, imagine a one-dimensional flow at a constant velocity and an injection of pollution at a constant rate. e. piston flow at the mean aquifer velocity, if the travelled distances are large with respect to the dimensions of the pollution source. (2) Laboratory studies and many field experiments yield local results, such as dispersion coefficients for instance. A real pollution may be rather extensive and a great amount of experiments, usually costly, will be required t o collect all the necessary characteristic parameters.
1] by deriving the moments of various orders of each of its terms: This system is then solved by induction, starting at n = 0. 41 is solved by the method of separation of variables and yields a countable sequence of solutions of the form: ui(y) exp (- wit), i = 0, 1,2 ,... 0 < ... < wi-l < wi < ... 3] is known from the solutions obtained for n < k . 41 ) and a particular solution of the complete equation. The general solution of the homogeneous equation: is a series Z i u i ( y ) exp (- w i t )defined previously.
Are well known in the pores, their boundary conditions are difficult to establish because of the high complexity of the boundary. 2) that modelling flow in a porous medium is to replace a system of well-known equations with simple conditions on very complex boundaries, by a system of equations with simple conditions on simple boundaries. We now see that to obtain the equivalence between the two systems is not a simple problem and probably still is an interesting field of research. , which is the approximation of an infinitesimal element of macroscopic medium in the sense we just defined) are twice continuously differentiable except at some points, curves and surfaces of the porous medium, which is not consistent with the assumption that these variables verify second-order partial differential equations everywhere.
Concepts of real analysis by Charles Hayes