  We prove in this short report the existence of a fundamental solution (F.S.)
for the Cauchy initial boundary problem on the whole space for the parabolic
differential equation having at origin the point of non-integrable unbounded
discontinuity for coefficient before a first order derivative.
  We give also the non-asymptotic rapidly decreasing at infinity estimate for
these function.
  We extend the classical parametrix method offered by E.E.Levi.
