Nonlinear Partial Differential Equations

Nonlinear Partial Differential Equations
Author: Mi-Ho Giga
Publisher: Springer Science & Business Media
Total Pages: 307
Release: 2010-05-30
Genre: Mathematics
ISBN: 0817646515

This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.

Nonlinear Dispersive Equations

Nonlinear Dispersive Equations
Author: Jaime Angulo Pava
Publisher: American Mathematical Soc.
Total Pages: 272
Release: 2009
Genre: Mathematics
ISBN: 0821848976

This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.

Metasolutions of Parabolic Equations in Population Dynamics

Metasolutions of Parabolic Equations in Population Dynamics
Author: Julián López-Gómez
Publisher: CRC Press
Total Pages: 372
Release: 2015-10-28
Genre: Mathematics
ISBN: 1482238993

Metasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. Highlighting the author's advanced work in the field, it covers the latest developments in the theory of nonlinear parabolic problems. The book reveals how to mathematically determine if a species maintains, dwindles, or increases under certain circumstances. It explains how to predict the time evolution of species inhabiting regions governed by either logistic growth or exponential growth. The book studies the possibility that the species grows according to the Malthus law while it simultaneously inherits a limited growth in other regions. The first part of the book introduces large solutions and metasolutions in the context of population dynamics. In a self-contained way, the second part analyzes a series of very sharp optimal uniqueness results found by the author and his colleagues. The last part reinforces the evidence that metasolutions are also categorical imperatives to describe the dynamics of huge classes of spatially heterogeneous semilinear parabolic problems. Each chapter presents the mathematical formulation of the problem, the most important mathematical results available, and proofs of theorems where relevant.

Equadiff IV

Equadiff IV
Author: J. Fabera
Publisher: Springer
Total Pages: 460
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540355197

Landau-Lifshitz Equations

Landau-Lifshitz Equations
Author: Boling Guo
Publisher: World Scientific
Total Pages: 414
Release: 2008
Genre: Mathematics
ISBN: 9812778756

This is a comprehensive introduction to Landau-Lifshitz equations and Landau-Lifshitz-Maxwell equations, beginning with the work by Yulin Zhou and Boling Guo in the early 1980s and including most of the work done by this Chinese group led by Zhou and Guo since. The book focuses on aspects such as the existence of weak solutions in multi dimensions, existence and uniqueness of smooth solutions in one dimension, relations with harmonic map heat flows, partial regularity and long time behaviors.The book is a valuable reference book for those who are interested in partial differential equations, geometric analysis and mathematical physics. It may also be used as an advanced textbook by graduate students in these fields.