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 <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>H</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msup> <mfenced open="(" close=")" separators="|"> <mrow> <mi>ℝ</mi> </mrow> </mfenced> </math> . If <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>D</mi> <mo>></mo> <mn>0</mn> </math> , the local well-posedness is given for <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>s</mi> <mo>></mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </math> and for <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mi>s</mi> <mo>></mo> <mn>3</mn> <mo>/</mo> <mn>2</mn> </math> if <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <mi>D</mi> <mo>=</mo> <mn>0</mn> </math> .
