Bücher der Reihe Monographs and Surveys in Pure and Applied Mathematics

Part of the "Pitman Monographs in Pure and Applied Mathematics" series, this text presents various problems of partial differential equations. It covers elliptic systems degenerated at the boundary, overdetermined boundary value problems and initial boundary value problems.

Presents the ray method for studying nonlinear wave propagation in fluid dynamics and plasma physics. Topics covered are shock wave propagation, the derivation of model equations in several dimensions (dissipative and dispersive) and the interaction of waves, both hyperbolic and dispersive.

Inverse boundary problems are an area of applied mathematics with applications throughout physics and the engineering sciences. This book considers the following: Can the unknown coefficients of an elliptic partial differential equation be determined from the eigen values and the boundary values of the eigen functions?

A monograph that examines a variety of phenomena in which interfaces play a crucial role. It studies developments related to the Marangoni effect, including patterned convection and instabilities, oscillatory/wavy phenomena, and turbulent phenomena.

Presents the theoretical framework for developing methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. This work is suitable for researchers in engineering as well as advanced students in these fields.

Examines periodic solutions of impulsive differential equations. Periodic linear impulsive differential equations, the use of the small parameter method in noncritical and critical cases, and the existence of periodic solutions of nonlinear differential equations are discussed.

Studies Cauchy problems that are not well-posed in the classical sense. This volume presents and examines three major approaches to treating such problems: semigroup methods, abstract distribution methods, and regularization methods.

This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics. This book makes up-to-date material accessible and lays the foundation for future advances.

This monograph is designed to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable self-contained introduction to linear and nonlinear scattering theory.

This, and a companion volume, provides an account of complex analytic methods for partial differential equations and their applications. The authors focus on applications in acoustics, fluid dynamics and wave motion.