We study a formation of patterns in Burgers-type equations endowed with a bounded but nonmonotonic dissipative flux: ut + f(u)x = ±vQ(ux)x, Q(s) = s/(1 + s2). Issues of uniqueness, existence, and smoothness of a solution are addressed. Asymptotic regions of a solution are discussed; in particular, classical and nonclassical traveling waves with an embedded subshock are constructed.
|Number of pages||31|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - May 1998|