BOUNDARY PROCEDURES FOR THE TIME-DEPENDENT BURGERS’ EQUATION UNDER UNCERTAINTY Dedicated to Professor James Glimm on the occasion of his 75th birthday

LESSER KNOWN MIRACLES OF BURGERS EQUATION∗ Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

This article is a short introduction to the surprising appearance of Burgers equation in some basic probabilistic models.

On stochastic differential equations and a generalised Burgers equation Dedicated to Professor Jia-an Yan on the Occasion of his 70th Birthday

In this paper, we discuss a link of Itô’s stochastic differential equations to nonlinear partial differential equations of Burgers type. Under certain conditions, we derive a generalised Burgers equation from a stochastic differential equation. We also give some economic interpretation of our result as well as the relevant conditions. Mathematics Subject Classification (2000): 60H10, 35K58, 91G99.

Unveiling the nature of supramolecular crown ether–C60 interactions† †This work is dedicated to Professor José Barluenga on the occasion of his 75th birthday. ‡ ‡Electronic supplementary information (ESI) available: Experimental procedures, titration experiments, MS spectra, electrochemistry experiments, transient absorption measurements and computational details. See DOI: 10.1039/c5sc00850f Click here for additional data file.

LINEAR WAVES THAT EXPRESS THE SIMPLEST POSSIBLE PERIODIC STRUCTURE OF THE COMPRESSIBLE EULER EQUATIONS∗ Dedicated to Professor James Glimm on the occasion of his 75th birthday

In this paper we show how the simplest wave structure that balances compression and rarefaction in the nonlinear compressible Euler equations can be represented in a solution of the linearized compressible Euler equations. Such waves are exact solutions of the equations obtained by linearizing the compressible Euler equations about the periodic extension of two constant states separated by entr...

KINETIC FUNCTIONS IN MAGNETOHYDRODYNAMICS WITH RESISTIVITY AND HALL EFFECT Dedicated to Professor James Glimm on the occasion of his 75th birthday

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal magnetohydrodynamics and includes second-order terms accounting for magnetic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting complex wave structures, including undercompressive nonclassical shock waves. We investigate numerically the subtle...