A. A. Samarskii – författare

This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches to the analysis of the models by traditional means of applied mathematics are described. Numerical methods for the approximate solution of steady and unsteady-state heat conduction problems are discussed. Investigation of difference schemes is based on the general stability theory. Much emphasis is put on problems in which phase transitions are involved and on heat and mass transfer problems. Problems of controlling and optimizing heat processes are discussed in detail. These processes are described by partial differential equations, and the main approaches to numerical solution of the optimal control problems involved here are discussed. Aspects of numerical solution of inverse heat exchange problems are considered. Much attention is paid to the most important applied problems of identifying coefficients and boundary conditions for a heat transfer equation. This first volume considers the mathematical models of heat transfer, classic analytical solution methods for heat conduction problems, numerical methods for steady-state and transient heat conduction problems, and phase change problems. The second volume presents solution techniques for complicated heat transfer problems (radiation, convection, thermoelasticity, thermal process control and inverse problems) as well as some examples of solving particular heat transfer problems.

This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches, to the analysis of the models by traditional means of applied mathematics are described. Numerical methods for the approximate solution of steady- and unsteady state heat conduction problems are discussed. Investigation of difference schemes is based on the general stability theory. Much emphasis is put on problems in which phase transitions are involved and on heat and mass transfer problems. Problems of controlling and optimizing heat processes are discussed in detail. These processes are described by partial differential equations, and the main approaches to numerical solution of the optimal control problems involved here are discussed. Aspects of numerical solution of inverse heat exchange problems are considered. Much attention is paid to the most important applied problems of identifying coefficients and boundary conditions for a heat transfer equation. The first volume considered the mathematical models of heat transfer, classic analytical solution methods for heat conduction problems, numerical methods for steady-state and transient heat conduction problems, and phase change problems. In this second volume, we present solution techniques for complicated heat transfer problems (radiation, convection, thermoelasticity, thermal process control and inverse problems) as well as some examples of solving particular heat transfer problems.

A Collection of Problems on Mathematical Physics is a translation from the Russian and deals with problems and equations of mathematical physics. The book contains problems and solutions. The book discusses problems on the derivation of equations and boundary condition. These Problems are arranged on the type and reduction to canonical form of equations in two or more independent variables. The equations of hyperbolic type concerns derive from problems on vibrations of continuous media and on electromagnetic oscillations. The book considers the statement and solutions of boundary value problems pertaining to equations of parabolic types when the physical processes are described by functions of two, three or four independent variables such as spatial coordinates or time. The book then discusses dynamic problems pertaining to the mechanics of continuous media and problems on electrodynamics. The text also discusses hyperbolic and elliptic types of equations. The book is intended for students in advanced mathematics and physics, as well as, for engineers and workers in research institutions.

No detailed description available for "Blow-Up in Quasilinear Parabolic Equations".

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.