Yuming Qin Knihy

This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science.

When they find the extra finger, forensic scientist Qin Ming and his team are stunned. How could there be eleven fingers but only one corpse? Though Qin Ming is no stranger to tough cases, he has never encountered one quite like this. With no answers and no leads, Qin Ming must turn his attention to the many other homicides waiting to be solved. His investigations take him to back-alley neighborhoods, the remote countryside, and even the expansive homes of the rich and elite. But now it seems that every case in Dragon City contains a misplaced body part. Is it a coincidence or a sick joke, or is the killer trying to send Qin Ming a message? As Qin Ming and the police force work to unravel each murder, a killer zeros in on him. Can Qin Ming track down the killer before he becomes the next victim?

This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.

This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i. e., differential, difference and integral equations.

Most of the material appears in book form for the first time Chapter 1 gives a survey of basic necessary knowledge for those working in the field of partial differential equations at graduate level Includes supplementary material: sn. pub/extras