Linear stability of shock profiles for a quasilinear Benney system in Double-struck capital R-2 x Double-struck capital R+

摘要

Following Dias et al. [Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws, J. Differential Equations 251 (2007) 555-563], we study the linearized stability of a pair (0,(V) over tilde), where (V) over tilde is a shock profile for a family of quasilinear hyperbolic conservation laws in R-2 x R+ coupled with a semilinear Schrodinger equation.