Linear and Semilinear Partial Differential Equations: An Introduction

ISBN-13: 9783110269048 / Angielski / Twarda / 2012 / 296 str.

Radu Precup

Opis

This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern theory and a master course in semi-linear equations.

Spis treści

PART I: Classical Theory

1 Preliminaries; 2 Partial differential equations and mathematical modeling; 3 Elliptic boundary value problems; 4 Mixed problems for evolution equations; 5 The Cauchy problem for evolution equations;

PART II: Modern Theory

6 Distributions; 7 Sobolev spaces; 8 Variational theory of elliptic boundary value problems;

PART III: Semi-linear Equations

9 Semi-linear elliptic problems; 10 Semi-linear heat equation; 11 Semi-linear wave equation; 12 Nonlinear Schrodinger equations.

O autorze

Radu Precup, Babes-Bolyai University of Cluj-Napoca, Romania.