On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems write by Sajan K. Samuel. This book was released on 2019. On Some Applications of the Maximum Principles to a Variety of Elliptic and Parabolic Problems available in PDF, EPUB and Kindle. "One of the most important and useful tools used in the study of partial differential equations is the maximum principle. This principle is a natural extension to higher dimensions of an elementary fact of calculus: any function, which satisfies the inequality f′′ > 0 on an interval [a,b], achieves its maximum at one of the endpoints of the interval. In this context, we say that the solution to the differential inequality f′′ > 0 satisfies a maximum principle. In this thesis we will discuss the maximum principles for partial differential equations and their applications. More precisely, we will show how one may employ the maximum principles to obtain information about uniqueness, approximation, boundedness, convexity, symmetry or asymptotic behavior of solutions, without any explicit knowledge of the solutions themselves. The thesis will be organized in two main parts. The purpose of the first part is to briefly introduce in Chapter 1 the terminology and the main tools to be used throughout this thesis. We will start by introducing the second order linear differential operators of elliptic and parabolic type. Then, we will develop the first and second maximum principles of E. Hopf for elliptic equations, respectively the maximum principles of L. Nirenberg and A. Friedman for parabolic equations. Next, in the second part, namely in Chapter 2 and 3, we will introduce various P-functions, which are nothing else than appropriate functional combinations of the solutions and their derivatives, and derive new maximum principles for such functionals. Moreover, we will show how to employ these new maximum principles to get isoperimetric inequalities, symmetry results and convexity results in the elliptic case (Chapter 2), respectively spatial and temporal asymptotic behavior of solutions, in the parabolic case (Chapter 3)."--Abstract.
Maximum Principles in Differential Equations
Maximum Principles in Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles in Differential Equations write by Murray H. Protter. This book was released on 2012-12-06. Maximum Principles in Differential Equations available in PDF, EPUB and Kindle. Maximum Principles are central to the theory and applications of second-order partial differential equations and systems. This self-contained text establishes the fundamental principles and provides a variety of applications.
Maximum Principles and Their Applications
Maximum Principles and Their Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles and Their Applications write by Sperb. This book was released on 1981-07-28. Maximum Principles and Their Applications available in PDF, EPUB and Kindle. Maximum Principles and Their Applications
Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems
Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems write by Gershon Kresin. This book was released on 2012-08-15. Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems available in PDF, EPUB and Kindle. The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.
Elliptic and Parabolic Problems
Elliptic and Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic and Parabolic Problems write by Catherine Bandle. This book was released on 2006-01-17. Elliptic and Parabolic Problems available in PDF, EPUB and Kindle. Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.
