A dynamical process of several variables

In the space of $\varphi$-distributions with values belonging to a Banach space, the process described by the problem of partial differential equation has been considered. Conditions under which the process is dynamic have been given. The notion of $\varphi$-distributions and $\varphi$-solutions has been introduced by V.S. Mokeichev as a tool for studying the solvability of some partial differential equations and mathematical models. Thus, it is possible to solve certain problems without any generalized solution (Schwartz distribution). Furthermore, an opportunity to explain the theory of solvability without assumptions on the type of the investigated partial differential equation (elliptic, parabolic, hyperbolic) and on whether the equation is scalar. One of principal advantages of the space of $\varphi$-distributions is that its elements and only they expand in the series by a given system of elements $\varphi$.