The book has two chapters. In the first, boundary value problems for the equations with varying time directions: \(u_ t sgn x=u_{xx}\), \(u_ t sgn x=u_{xx}+(k/x)u_{xx}\), \(u_ t=xu_{xx}+\alpha u_ x\), in the domain \(Q=(| x| <\infty)\times (0,\pi),\) are formulated and solved. The study of these problems is performed using the potential theory and the theory of some equations with singularities.
In the second chapter the properties of some heat potentials are presented in connection with the Bessel operator \(B=\partial^ 2/\partial y^ 2+(k/y)\partial /\partial y\) and the estimations of their norms in various spaces.