### Equivalence Problem for The Canonical Form of Linear Second Order Parabolic Equations

#### Abstract

The article is devoted to the equivalence problem for the class of linearsecond order parabolic equations, the first\begin{equation}\label{first equ}u_t = u_{xx} + a(x)u,\end{equation}and\begin{equation}\label{second equ}u_t = u_{xx} + \frac{k}{{x^2 }}u\end{equation}$k$ a nonzero constant. Conditions which the parabolic equation\begin{equation}\label{parabolic eq}%u_t + a\left( {t,x} \right)u_{xx} + b\left( {t,x} \right)u_x + c\left( {t,x} \right)u = 0a_1\left( {t,x} \right)u_t + a_2\left( {t,x} \right)u_x + a_3\left( {t,x}\right)u + u_{xx}= 0\end{equation}to be equivalent to (0.1)-(0.2) are obtained

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