A Semilinear Heat Equation with Singular Nonlinearity
Author: M. Loayza
Publisher:
Published: 2004
Total Pages: 24
ISBN-13:
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The Heat Equation with Singular Nonlinearity and Singular Initial Data
Author: M. Loayza
Publisher:
Published: 2005
Total Pages: 26
ISBN-13:
DOWNLOAD EBOOKMathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS
Author: Pierpaolo Esposito
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 338
ISBN-13: 0821849573
DOWNLOAD EBOOKMicro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. This title offers an introduction to many methods of nonlinear analysis and PDEs through the analysis of a set of equations that have enormous practical significance.
Superlinear Parabolic Problems
Author: Pavol Quittner
Publisher:
Published: 2007
Total Pages: 0
ISBN-13: 9780817684419
DOWNLOAD EBOOK"This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology." "The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics." -- Book Jacket.
Patterns of Dynamics
Author: Pavel Gurevich
Publisher: Springer
Published: 2018-02-07
Total Pages: 411
ISBN-13: 3319641735
DOWNLOAD EBOOKTheoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.
Mathematics for Nonlinear Phenomena — Analysis and Computation
Author: Yasunori Maekawa
Publisher: Springer
Published: 2017-11-01
Total Pages: 335
ISBN-13: 3319667645
DOWNLOAD EBOOKThis volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.
Handbook of Differential Equations: Evolutionary Equations
Author: C.M. Dafermos
Publisher: Elsevier
Published: 2005-10-05
Total Pages: 677
ISBN-13: 0080461387
DOWNLOAD EBOOKThe aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
Non-Local Partial Differential Equations for Engineering and Biology
Author: Nikos I. Kavallaris
Publisher: Springer
Published: 2017-11-28
Total Pages: 310
ISBN-13: 3319679449
DOWNLOAD EBOOKThis book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.
Nonlinear Partial Differential Equations
Author: Mi-Ho Giga
Publisher: Springer Science & Business Media
Published: 2010-05-30
Total Pages: 307
ISBN-13: 0817646515
DOWNLOAD EBOOKThis 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.
Inequalities Involving Functions and Their Integrals and Derivatives
Author: Dragoslav S. Mitrinovic
Publisher: Springer Science & Business Media
Published: 1991-07-31
Total Pages: 606
ISBN-13: 9780792313304
DOWNLOAD EBOOKThis volume provides a comprehensive, up-to-date survey of inequalities that involve a relationship between a function and its derivatives or integrals. The book is divided into 18 chapters, some of which are devoted to specific inequalities such as those of Kolmogorov-Landau, Wirtinger, Hardy, Carlson, Hilbert, Caplygin, Lyapunov, Gronwell and others. Over 800 references to the literature are cited; proofs are given when these provide insight into the general methods involved; and applications, especially to the theory of differential equations, are mentioned when appropriate. This volume will interest all those whose work involves differential and integral equations. It can also be recommended as a supplementary text.
