Essentials of Partial Differential Equations - Öchsner, Andreas

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Résumé :
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. ...

Biographie:
Sorin Vlase is a Full Professor of Mechanics (1996) at Transylvania University of Br?ov, Romania. He obtained his Dipl.-Ing degree in Automotive Engineering at the Transylvania University of Br?ov(1976) and a licence in Mathematics at the University of Bucharest (1982). He was researcher at the Truck Factory ROMAN SA (1976-1978) and at the Research Center in Automotive Engineering INAR SA (1978-1980). He become Doctor in Engineering Sciences (Mechanics) in 1989 and obtain his habilitation in Automotive Engineering at the University of Pitesti (Dr.-hab.) in 2014. From 2012 become member of the Romanian Academy of Technical Science. In 2004 he become the Head of the Department of Mechanical Egineering at the Faculty of Mechanical Engineering in the Transylvania University where he still work. Marin Marin is a Full Professor of Mathematics at Department of Mathematics and Computer Science, Transilvania University of Brasov, Romania. Andreas ?chsner is a Full Professor of Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. Having obtained his Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), Germany, he subsequently served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003 while working to complete his Doctor of Engineering Sciences (Dr-Ing.) degree. From 2003 to 2006, he was an Assistant Professor at the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007-2013) as a Full Professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also Head of the Advanced Materials and Structure Lab. From 2014 to 2017 he was a Full Professor at the School of Engineering, Griffith University, Australia and Leader of the Mechanical Engineering Program (Head of Discipline and Program Director). ...

Sommaire:

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.

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