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 ℝ . If D > 0 , the local well-posedness is given for s > 1 / 2 and for s > 3 / 2 if D = 0 .