EMS Series of Lectures in Mathematics
1 total work
Splitting Methods for Partial Differential Equations with Rough Solutions
by Helge Holden, Kenneth H. Karlsen, and Knut-Andreas Lie
Published 30 April 2010
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks.