Some Constructive Aspects of the Theory of Hyperbolic Equations

摘要

The relative significance of the stability of difference schemes that are consistent with a hyperbolic differential equation is examined within the context of various L(p) spaces. The usefulness of identifying 'modified equations' which model the behavior of the difference schemes better than the original equation, even in the case of non-smooth data is also discussed. A scalar conservation law is singled out to emphasize the importance of establishing a meaningful extension of the notion of stability to the nonlinear case.