Generalized solutions to singular initial-boundary hyperbolic problems with non-lipshitz nonlinearities
Global in Time Stability of Steady Shocks in Nozzles
We prove global dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. One of the key improvements compared with previous results is that we assume neither the smallness of the slope of the nozzle nor the weakness of the shock strength. A key ingredient of the proof are the derivation a exponentially decaying energy estimates for a linearized problem.
Global solution to a Hopf equation and its application to non-strictly hyperbolic systems of conservation laws.
Global sound waves for quasilinear second order wave equations.