Title: Stationary solution to outflow/inflow problems to a symmetric system
of hyperbolic-parabolic conservation laws

Speaker: Prof. Shinya Nishibata, Tokyo Institute of Technology

Time: June 4th, 4:00-5:00pm, 2018

Place: South Building No. 613

Abstract: In this talk, we discuss a large time behavior of a solution to a
coupled system of viscous and inviscid conservation laws over one-dimensional half space. 
 The purpose of research is to show an existence of a stationary solution 
and its asymptotic stability under assuming the existence
of an entropy function. This assumption enables us to transform the original
system to a symmetric hyperbolic-parabolic systems.
In asymptotic analysis, we derive an a priori  estimate by an energy method.
In order to derive the basic estimate, we make use of an energy form,
which is obtained by substituting the stationary solution in the entropy function.
The symmetric system is utilized in deriving the  estimates of the higher order derivatives of solutions.
In this procedure, we suppose that the stability condition hold at spatial far field.