Nonlinear Stability

The present volume gives a very modern treatment of all theoretical as well as computational aspects of nonlinear structural stability.

This paper proves that certain non-classical shock waves in a rotationally invariant system of viscous conservation laws posses nonlinear large-time stability against sufficiently small perturbations. The result applies to small intermediate magnetohydrodynamic shocks in the presence of dissipation.

New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals.

by Philippe G Lefloch (Author),‎ Yue Ma (Author)

This book presents powerful modern control techniques based on the parallelism and adaptive capabilities of biological nervous systems. The book builds systematically from actuator nonlinearities and strict feedback in nonlinear systems to nonstrict feedback, system identification, model reference adaptive control, and novel optimal control using the Hamilton-Jacobi-Bellman formulation. The author concludes by developing a framework for implementing intelligent control in actual industrial systems using embedded hardware.

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles.