Local Well-Posedness to the Cauchy Problem for an Equation of the Nagumo Type

Abstract

In this paper, we show the local well-posedness for the Cauchy problem for the equation of the Nagumo type in this equation (1) in the Sobolev spaces $H^s\left(ℝ\right)$ . If $D>0$ , the local well-posedness is given for $s>1/2$ and for $s>3/2$ if $D=0$ .