## Mathematics Publications

Mathematics

Article

#### Publication Version

Published Version

1988

#### Journal or Book Title

SIAM Journal on Mathematical Analysis

19

2

312

336

10.1137/0519023

#### Abstract

In this paper, we present several results concerning the long-time behavior of positive solutions of Burgers’ equation $u_t = u_{xx} + \varepsilon uu_x$, $0 < x < 1$, $t > 0$, $u(x,0)$ given, subject to one of two pairs of boundary conditions: (A) $u(0,t) = 0$, $u_x (1,t) = au^p (1,t)$, $t > 0$, or (B) $u(1,t) = 0$, $u_x (0,t) = - au^p (0,t)$, where $0 < p < \infty$. A complete stability-instability analysis is given. It is shown that some solutions can blow up in finite time. Generalizations replacing $\varepsilon uu_x$ by $(f(u))_x$ and $au^p$ by $g(u)$ are discussed.

This is an article from SIAM Journal on Mathematical Analysis 19 (1988): 312, doi:10.1137/0519023. Posted with permission.

Society for Industrial and Applied Mathematics

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