Scalar Conservation Laws

Giuseppe Maria Coclite (Autor)

Buch | Softcover

148 Seiten

2024 | 2024 ed.
Springer Verlag, Singapore
978-981-97-3983-7 (ISBN)

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This book are notes prepared for the PhD courses that the author has been teaching during the last 10 years. The material available in the already existing literature (papers and essays) has been collected in this unique text, presenting the results with all the details for the reader’s convenience, fixing a unified notation, and providing a consistent framework for the subject. These notes cover many of the arguments that usually can be found in high level essays, where the proofs are simply sketched, and in papers, which are not easily available and not always self-contained.
This book is intended for1. PhD students in Mathematics, Physics and Mechanical Engineering in order to learn the basic features of nonlinear scalar equations,2. researchers interested in nonlinear hyperbolic PDEs in order to learn the details behind some known and deep results on nonlinear scalar equations,3. teachers of courses on nonlinear PDEs.The readers are expected to know the basic measure theory and Sobolev spaces.

Dr. Giuseppe Maria Coclite, Full Professor in Mathematical Analysis at the Department of Mechanics, Mathematics and Management of the Polytechnic University of Bari (Italy). His main research interests are Boundary Controllability for Systems of Conservation Laws, Traffic Models, Parabolic equations, Conservation laws with discontinuous flows, Nonlocal models in continuum mechanics, optimization in measure spaces, etc.

Chapter 1 Introduction.- Chapter 2 Entropy Solutions.- Chapter 3 Riemann Problem.- Chapter 4 Functions with Bounded Variation.- Chapter 5 Wave Front Tracking.- Chapter 6 Vanishing Viscosity.- Chapter 7 Compensated Compactness.- Chapter 8 Periodic solutions.- Chapter 9 Oleinik Estimate.- Chapter 10 Lax-Oleinik Formula.

Erscheinungsdatum	12.07.2024
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	20 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	asymptotics of periodic solutions • BV functions • Characteristics • compensated compactness • Fluid dynamic • front tracking • Lax-Oleinik formula • Oleinik estimate • Shock waves • vanishing viscosity
ISBN-10	981-97-3983-7 / 9819739837
ISBN-13	978-981-97-3983-7 / 9789819739837
Zustand	Neuware