Product Description: This book presents the theory of hyperbolic conservation laws from basic theory to the forefront of research. The text treats the theory of scalar conservation laws in one dimension in detail, showing the stability of the Cauchy problem using front tracking...read more

Product Description: William T. Sha first proposed the novel porous media formulation in an article in Nuclear Engineering and Design in 1980. The novel porous media formulation represented a new, flexible, and unified approach to solve real-world engineering problems...read more

Product Description: The local structure of solutions of initial value problems for nonlinear systems of conservation laws is considered. Given large initial data, there exist systems with reasonable structural properties for which standard entropy weak solutions cannot be continued after finite time, but for which weaker solutions, valued as measures at a given time, exist...read more

Product Description: This book is devoted to macroscopic models for traffic on a network, with possible applications to car traffic, telecommunications and supply-chains. The rapidly increasing number of circulating cars in modern cities renders the problem of traffic control of paramount importance, affecting productivity, pollution, life-style etc...read more

Product Description: Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally...read more

Product Description: The schemes are analyzed regarding their nonlinear stability Recently developed entropy schemes are presented A formalism is introduced for source terms

Product Description: We consider the Cauchy problem for a strictly hyperbolic $2\times 2$ system of conservation laws in one space dimension $u_t+[F(u)]_x=0, u(0,x)=\bar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields...read more

Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials. (view table of contents)

(view table of contents)

Product Description: During the last decade enormous progress has been achieved in the field of computational fluid dynamics. This became possible by the development of robust and high-order accurate numerical algorithms as well as the construc­ tion of enhanced computer hardware, e...read more

Product Description: 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...read more (view table of contents, read Amazon.com's description)

Product Description: This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions...read more (view table of contents, read Amazon.com's description)

Product Description: This book presents the theory of hyperbolic conservation laws from basic theory to the forefront of research. The text treats the theory of scalar conservation laws in one dimension in detail, showing the stability of the Cauchy problem using front tracking...read more (view table of contents, read Amazon.com's description)

Product Description: This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws). These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline...read more (view table of contents, read Amazon.com's description)

(view table of contents)

(view table of contents)

(view table of contents)

Product Description: This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research...read more (view table of contents, read Amazon.com's description)

(view table of contents)