Differential Equations: Inverse and Direct Problems [Paperback]

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.Degenerate first order identification problems in Banach spaces. A non-isothermal dynamical Ginzburg-Landau model of superconductivity. Some global in time results for integrodifferential parabolic inverse problems. Fourth order ordinary differential operators with general Wentzell boundary conditions. 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 equa-
tion of viscoelasticity. Asymptotic behavior of a phasl,