Inverse boundary problems are a rapidly developing area of applied mat hematics, and inverse boundary spectral problems (IBSP) constitute an important and distinct part of the field because of the special charac ter of the data involved, the specific methods used to deal with that data, and their relevance to applications, including medical imaging and geophysical prospecting. Although the theory of IBSP has been in d evelopment for at least 10 years, until now the literature has been sc attered throughout various journals. This self-contained monograph sum marizes IBSP concepts and the...

Written by leading researchers in the field, this focused collection of articles on the physics of porous media begins with a discussion of mathematical methods to be used, then examines various aspects of the physical theory. This field is of interest to mathematicians concerned with flow through porous media, which is usually related to recovery of oil from oil wells or to underground water percolation.

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.
The...

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.
The...

The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Compactness Method gathers together into a single volume the essential ideas and developments.
The authors begin with the fundamental theorems, then consider the Cauchy problem of the scalar equation, build a framework for L8 estimates of viscosity...

This Research Note addresses several pivotal problems in spectral theo ry and nonlinear functional analysis in connection with the analysis o f the structure set of zeroes of a general class of nonlinear operator s. Appealing to a broad audience, it contains many important contribut ions to linear algebra, linear functional analysis, nonlinear function analysis, and topology. The author gives several applications of the abstract theory to reaction diffusion equations and system. The result s presented cover a thirty-year period and cut across a variety of mat hematical fields.

Interfacial Phenomena and Convection remedies this problem by furnishi ng a self-contained monograph that examines a rich variety of phenomen a in which interfaces pay a crucial role. From a unified perspective t hat embraces physical chemistry, fluid mechanics, and applied mathemat ics, the authors study recent developments related to the Marangoni ef fect, including patterned convection and instabilities, oscillatory/wa nard layers subj ected to transverse and longitudinal thermal gradients and phenomena i nvolving surface tension gradients as the driving forces, including fa lling films,...