Is there a name for the PDE resembles a "reversed" heat/diffusion equation $\frac{\partial^{2} u}{\partial t^{2}} = \frac{\partial u}{\partial x}$?

Question

Is there a name for the second-order linear Partial Differential Equation of the form $\frac{\partial^{2} u}{\partial t^{2}} = \frac{\partial u}{\partial x}$ which resembles the heat/diffusion equation but its space and time derivatives have switched orders (i.e. the time is the 2nd derivative while the space is 1st order derivative)?

Answer 1

If the space is one-dimensional, is there really a mathematical distinction between time and space? I would still call this the heat equation, except it happens to have different variable names than conventional.

But be explicit about the swap if you are to present this to anyone. Just to make them aware of it, or if they notice on their own, so that they understand it's not a typo.