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

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.