STABILITY OF TRAVELING WAVES FOR NONCONVEX SCALAR VISCOUS CONSERVATION-LAWS

Travelling waves of a viscous conservation law (so-called viscous profiles) are shown to be stable in polynomialy weighted L(infinity) spaces. There is no assumption of convexity on the nonlinear term and thus earlier results of Il'in and Oleinik, Sattinger, and Kawashima and Matsumura are generalized. The method uses the semigroup of the linearized equation with solutions of the full problem expressed by the variation of constants formula. Estimates are derived for the semigroup through a new technique for estimating the resolvent.