This book presents the theory of hyperbolic conservation laws from basic
theory to the forefront of research.
The text treats the theory of scalar conservation laws in one dimension
in detail, showing the stability of the Cauchy problem using front
tracking. The extension to multidimensional scalar conservation laws is
obtained using dimensional splitting. Inhomogeneous equations and
equations with diffusive terms are included as well as a discussion of
convergence rates, and coverage of the classical theory of Kruzkov and
Kuznetsov. Systems of conservation laws in one dimension are treated in
detail, starting with the solution of the Riemann problem.
The book includes detailed discussion of the recent proof of
well-posedness of the Cauchy problem for one-dimensional hyperbolic
conservation laws, and a chapter on traditional finite difference
methods for hyperbolic conservation laws with error estimates and a
section on measure valued solutions.