The third mixed problem for the Sonin equation in a half space

Abstract

We consider follwing mixed boundary-value problem: $$\begin{array}{*{20}c} {u'_t (t,R) + xu'_y (t,R) + yu'_z (t,R) = u''_{x^2 } (t,R) + f(t,R)} \\ {in \Pi _T = \{ (t,R),0< t \leqslant T,R = (x,y,z),R \in E_3 ,0< x\} ,} \\ {u(0,R) = u_0 (R),u'_x (t,0,y,z) + \beta (t)u(t,0,y,z) = g(t,y,z).} \\ \end{array}$$ A solution of this problem is obtained in the form of a potential.