Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 443-473 |
Number of pages | 31 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 51 |
Issue number | 5 |
DOIs | |
State | Published - May 1998 |