Differential Equations : Inverse and Direct Problems book cover
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Differential Equations
Inverse and Direct Problems




ISBN 9781584886044
Published June 9, 2006 by Chapman and Hall/CRC
294 Pages - 50 B/W Illustrations

 
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Book Description

With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientific fields.

Exploring the hypotheses and numerical approaches that relate to pure and applied mathematics, this collection of research papers and surveys extends the theories and methods of differential equations. The book begins with discussions on Banach spaces, linear and nonlinear theory of semigroups, integrodifferential equations, the physical interpretation of general Wentzell boundary conditions, and unconditional martingale difference (UMD) spaces. It then proceeds to deal with models in superconductivity, hyperbolic partial differential equations (PDEs), blowup of solutions, reaction-diffusion equation with memory, and Navier-Stokes equations. The volume concludes with analyses on Fourier-Laplace multipliers, gradient estimates for Dirichlet parabolic problems, a nonlinear system of PDEs, and the complex Ginzburg-Landau equation.

By combining direct and inverse problems into one book, this compilation is a useful reference for those working in the world of pure or applied mathematics.

Table of Contents

DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES

A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMS

SOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMS

FOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITION

STUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACES

DEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE

EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONS

CONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY

ASYMPTOTIC BEHAVIOR OF A PHASE FIELD SYSTEM WITH DYNAMIC BOUNDARY CONDITIONS

THE POWER POTENTIAL AND NONEXISTENCE OF POSITIVE SOLUTIONS

THE MODEL-PROBLEM ASSOCIATED TO THE STEFAN PROBLEM WITH SURFACE TENSION: AN APPROACH VIA FOURIER-LAPACE MULTIPLIERS

IDENTIFICATION PROBLEMS FOR NONAUTONOMOUS DEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE WITH DIRICHLET BOUNDARY CONDITIONS

EXISTENCE RESULTS FOR A PHASE TRANSITION MODEL ON MICROSCOPIC MOVEMENTS

STRONG L2-WELLPOSEDNESS IN THE COMPLEX GINZBURG-LANDAU EQUATION

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Reviews

"…Almost all of the fourteen contributions contain original results; they do not just survey or explain results already published elsewhere. They cover a wide scope of up-to-date topics from the field of differential equations. … The book will be an interesting and stimulating read for research workers in the field."
-EMS Newsletter, June 2007