Pointwise bounds in parabolic and elliptic partial differential equations /

A method is presented for obtaining explicit upper and lower pointwise bounds for the solution of rather general interior boundary value problems. The differential equations associated with these problems are of the elliptic type in certain sections while both linear and non-linear parabolic equations are the subject of investigation in other sections. The bounds which are obtained are in terms of the integrals of the squares of known functions and hence, in the linear case, improvement is possible using the Rayleigh-Ritz technique."This paper was submitted as a Thesis in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The research was completed while the author attended the University of Maryland under the sponsorship of the U. S. Naval Postgraduate School. The assertions contained herein are those of the author and are not to be constructed as official or reflecting the views of the Navy Department or the naval service at large.""The author is indebted to Professor L. E. Payne for valuable advice and suggestions."Research supported by the United States Air Force and performed by the University of Maryland, College Park, Institute for Fluid Dynamics and Applied Mathematics.Institute for Fluid Dynamics and Applied Mathematics Technical Note No. BN-246.AD0256984. (from http://www.dtic.mil)."May, 1961."Includes bibliographical references (pages 146-148).A method is presented for obtaining explicit upper and lower pointwise bounds for the solution of rather general interior boundary value problems. The differential equations associated with these problems are of the elliptic type in certain sections while both linear and non-linear parabolic equations are the subject of investigation in other sections. The bounds which are obtained are in terms of the integrals of the squares of known functions and hence, in the linear case, improvement is possible using the Rayleigh-Ritz technique.This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research under Contract No.Mode of access: Internet