Center stable manifolds for quasilinear parabolic pde and conditional stability of nonclassical viscous shock waves
نویسنده
چکیده
Motivated by the study of conditional stability of traveling waves, we give an elementary H2 center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a carefully chosen implicit fixed-point scheme and straightforward time-weighted Hs energy estimates. As an application, we show conditional stability of Laxor undercompressive shock waves of general quasilinear parabolic systems of conservation laws by a pointwise stability analysis on the center stable manifold.
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