Pointwise Green's function bounds for multidimensional scalar viscous shock fronts
The authors study the stability of multidimensional scalar viscous shock fronts. They extend the pointwise semigroup method introduced in the one-dimensional case by one of the authors and others to the multidimensional case. A pointwise bound for the Green's function of the linearized operator is obtained. Based on this result the authors also sharpen some \(L^p\)-estimates obtained by \textit{J. Goodman} and \textit{J. R. Miller} [J. Dyn. Differ. Equ. 11, 255-277 (1999; Zbl 0934.35093)].
scientific article; zbMATH DE number 1836800