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

Ekkarath Thailert

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