Asymptotic analysis of nonlinear elliptic and parabolic singular perturbations
Abstract
Some classes of Nonlinear Second Order Elliptic and Parabolic Partial Differential Operators affected by the presence of a small parameter epsilon are investigated. The reduced problem (epsilon = 0) is characterized by the appearence of a free boundary of the solutions. The Existence, Uniqueness and regularity results are established for both perturbed and reduced problems. Sharp twosided estimates for the difference of the solutions of the perturbed and reduced problems are proved and some constructive procedures are found out for localizing and computing the free boundary of the reduced problem. The Kinetic Theory of membranes with enzymotic activity is one of the possible fields of applications of the results established, the small parameter being the socalled Michaelis' coefficient.
 Publication:

Final Technical Report
 Pub Date:
 September 1985
 Bibcode:
 1985kath.rept.....F
 Keywords:

 Asymptotic Series;
 Cauchy Problem;
 Free Boundaries;
 Nonlinear Equations;
 Partial Differential Equations;
 Perturbation;
 Calculus Of Variations;
 Convergence;
 Independent Variables;
 Kinetic Theory;
 Membranes;
 Operators (Mathematics);
 Solutions;
 Physics (General)