Linear and Quasi-linear Equations of Parabolic Type

Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions. In this volume boundary value problems are studied from two points of view; solvability, unique or otherwise, and the effect of various smoothness properties of the given functions on the smoothness of the solutions. There are seven chapters contained in this volume. Chapter One gives a statement of the new results and an historical sketch. Chapter Two introduces the various function spaces typical of modern Russian-style functional anaylsis. Chapters Three and Four deal with linear equations. Chapter Six concerns itself with quasilinear equations, and Chapter Seven with systems of equations. These last four chapters can be read independently of one another. Cover Title page Preface Prefatory Note to the Translation Contents Editor’s note Introductory material Auxiliary propositions Linear equations with discontinuous coefficients Linear equations with smooth coefficients Quasi-linear equations with principal part in divergence form Quasi-linear equations of general form Systems of linear and quasi-linear equations Bibliography Back Cover