Written by two international experts in the field, this book is the first unified survey of the advances made
in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This
reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used
to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions
on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part
of the boundary.
The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward
in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic
equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other
relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations,
the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes
equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and
the overcoming Holder continuity and image restoration.
Key Features
Provides the first unified survey of the advances made in the last 15 years in the field
Includes an up-to-date compendium of the mathematical literature on these topics