응용수학 세미나

연사 : 송경우교수 (경희대학교 수학과)
제목 : Semi-hyperbolic patches of solutions of the pressure-gradient system
일시 : 2008.10.30 (목) 오후 4:30
장소 : 산업경영학동 3층 세미나실 3321호

초록:  We introduce the pressure-gradient system in two space dimensions from the 2-D full Euler system. In the self-similar coordinates, the pressure-gradient system has a second-order equation for the pressure. We consider elliptic and hyperbolic problems arising from the four-wave Riemann problem of the system. In particular, for hyperbolic problems we construct patches of self-similar solutions, in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves, to the pressure gradient system. This type of solutions is common in the solutions of two-dimensional Riemann problems, as seen from numerical experiments. They are not determined by the hyperbolic domain of determinacy in the traditional sense. They are middle-way between the fully hyperbolic (supersonic) and elliptic region, which we call semi-hyperbolic or partially hyperbolic. Our intention is to use the patches as building tiles to construct global solutions to general Riemann problems.
제목 :  Semi-hyperbolic patches of solutions of the pressure-gradient system