Essentials of Partial Differential Equations

This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject.

Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green's function, and Green's formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects ofthe theory of partial differential equations.

Offers a two-step approach to partial differential equations: first an introduction to the theory and then modern problems Presents all the important classical notions: differential operators, characteristic surfaces, Levi functions, and Green's theory Includes the main initial boundary value problems associated with elliptic, parabolic, and hyperbolic equations

Autorentext

Marin Marin is Professor at the Department of Mathematics and Computer Science of the Transilvania University of Brasov.

Andreas Öchsner (born 19 October 1970) is a Professor and Head of Discipline in Mechanical Engineering at Griffith University, Queensland, Australia, and is also a Conjoint Professor at the Centre for Mass and Thermal Transport in Engineering Materials at the University of Newcastle (Australia). He is the author and co-author of over 150 refereed journal papers, more than 70 conference papers and 15 book chapters in the area of advanced materials and structures. Furthermore, he is the author and co-author of five books and 13 research monographs.

Inhalt
PART I: Quasilinear equations.- Operators of second order.- The theory of potential.- Elliptic operators.- Operational calculus.- Parabolic equations.- Hyperbolic equations.- Part II: Elements of distributions.- Integral formulas.- Equations of the first order.- Equations of second order.- Harmonic functions.- Weak solutions.- Regularity of the solutions.- Parabolic equations.- Hyperbolic equations.