Higher-Order Operators on Networks: Hyperbolic and Parabolic Theory

Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 22 systems of genuinely nonlinear hyperbolic balance laws in 1-D with a strong dissipative term. A diierent method, which combines the div-curl lemma with accretive ope...

Operators of higher order

Motivated by results on interactive proof systems we investigate the computational power of quantifiers applied to well-known complexity classes. In special, we are interested in existential, universal and probabilistic bounded error quantifiers ranging over words and sets of words, i.e. oracles if we think in a Turing machine model. In addition to the standard oracle access mechanism, we also ...

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS

Strehl Ratio with Higher-Order Parabolic Filter

Regularity Theory for Parabolic Nonlinear Integral Operators

Received by the editors March 8, 2010 and, in revised form, August 2, 2010, October 26, 2010, and December 17, 2010. 2010 Mathematics Subject Classification. Primary 35B65, 45G05, 47G10.