Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation
Abstract
We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation ut+uux+uuy= u, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, seperated by a curve y=(x), and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. Furthermore, we also get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large.
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