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
"…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