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Analytical Approaches to Multidimensional Balance Laws

Editat de Olga S. Rozanova
en Limba Engleză Hardback – 4 feb 2007
It is difficult to overestimate the importance of mathematical investigation of balance laws. They arise in many areas of physics, mechanics, chemistry, biology, social sciences. In this collective book we concentrate in particular on the equations of continuous medium and related to them. As a rule, they are very complicated in their primitive form. An important feature of such equations is a possible formation of singularities even in initially smooth solution within a finite time. The structure of the singularities can be very complex. A natural step in the approach to this problem is the transition, despite the three-dimensionality of our world, to spatially one-dimensional model. Significant progress has been achieved in this direction. Unfortunately, the methods of the one-dimensional theory, as usual, cannot be adapted to a case of many spatial variables. However, there are many attempts to deal with multidimensional problems. We would like to present some of them. All of the papers are written by outstanding experts, representing various schools in mathematics and mechanics. Each paper is organised as follows: it contains an elementary (as far as it is possible) introduction to a problem, a brief review of previously published results, and then original results of the authors are presented.
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Specificații

ISBN-13: 9781594543074
ISBN-10: 1594543070
Pagini: 246
Ilustrații: tables & charts
Dimensiuni: 189 x 262 x 21 mm
Greutate: 0.7 kg
Ediția:New.
Editura: Nova Science Publishers Inc

Cuprins

Preface; Probabilistic Interpretation of the vv-method for PDE Systems; On the Delta-Shock Front Problem; Singular Vortex in Hydro- and Gas Dynamics; The Investigation of a Regularised Model for the Motion of a Viscoelastic Medium; Singular Limits for the Riemann Problem: General Diffusion, Relaxation, and Boundary Conditions; On Kinetic Formulation of Measure Valued Solutions for Hyperbolic First-Order Quasilinear Equations with Several Space Variables; On Global Solutions of Multi-Dimensional Compressible Fluid Flows; Index.