An L¹ bound for |u_x (t,x) | in a one-dimensional parabolic conservation system

Abstract

This paper reports an L¹ bound for |u^xt,x | in a one dimensional parabolic system of conservation laws that is used elsewhere 3,4 when establishing global existence and optimal decay estimates by means of entropy flux pairs for the system where u = u₁,...,u_n ^T and f u = f₁u,...,f_nu ^T are n ×1 column vectors, with f u a smooth function defined in a ball of radius r centered at a fixed vector ūε Rⁿ, and ε >0 is a constant.

Keywords:

• Parabolic conservation system
• global estimates
• entropy flux pairs

AMS:

• 35K55