Partial differential equations : classification, properties and applications / Deborah E. Richards, editor.

Format:

Book

Contributor:

Richards, Deborah E., editor.

Series:

Mathematics research developments series.

Mathematics research developments

Language:

English

Subjects (All):

Differential equations, Partial.

Physical Description:

1 online resource (225 p.)

Place of Publication:

Hauppauge, New York : Nova Science Publishers, Incorporated, [2015]

Language Note:

English

Summary:

This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.

Contents:

PARTIAL DIFFERENTIAL EQUATIONS: CLASSIFICATION, PROPERTIES AND APPLICATIONS; PARTIAL DIFFERENTIAL EQUATIONS: CLASSIFICATION, PROPERTIES AND APPLICATIONS; Library of Congress Cataloging-in-Publication Data; CONTENTS; PREFACE; Chapter 1: THE LAX-MILGRAM THEOREM AND SOME APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS; Abstract; 1. Introduction; 2. The Lax-Milgram Theorem; 3. Some Applications of the Theorem to Partial Differential Equations; 4. Consequences for Applications and Summary

Chapter 2: COUPLED PDES AND CONTROL SYSTEMS ARISING IN CLIMATE DYNAMICS: OCEAN-ATMOSPHERE INTERACTIONS AND TROPICAL INSTABILITY WAVESAbstract; 1. Introduction and Mathematical Setting of the Problem; 2. Variational Formulation and Some Properties; 3. Existence and Uniqueness of Solution; 4. Study of Control Framework; 5. Conclusion and Comments; Appendix. Some Sobolev Imbedding Theorems and Fundamental Inequalities; References; Chapter 3: INTEGRATION OF PDE WITH THE HELP OF ANALYSIS OVER OCTONIONS AND CAYLEY-DICKSON ALGEBRAS; Abstract; 1. Introduction

2. PDE and Their Systems of Diverse Types over Octonions3. Line Integration and First and Second Order PDE over Cayley-Dickson Algebras; 4. Multidimensional Laplace Transforms over Cayley-Dickson Algebras and PDE; 5. Integration of Vector Sobolev Type PDE Over Octonions; 6. Integration of Vector Hydrodynamical PDE Over Octonions; References; Chapter 4: MIXED BOUNDARY-VALUE PROBLEM FOR DIVERGENT HYPERBOLIC PDE: EXISTENCE AND PROPERTIES OF SOLUTIONS, APPLICATIONS IN SEQUENTIAL OPTIMAL CONTROL WITH POINTWISE IN TIME STATE CONSTRAINTS; Abstract; 1. Introduction

2. Existence and Properties of Solutions of Divergent Hyperbolic Partial Differential Equations3. Sequential Optimization for Semilinear Divergent Hyperbolic Equation with Pointwise in Time State Constraints and with Mixed Boundary Conditions; References; INDEX; Blank Page

Notes:

Includes index.

Description based on print version record.

ISBN:

1-63482-754-6