I am studying the Volume 3 (Theory of Differential Equations) of the book Generalized Functions written by I. M. Gel'Fand and G. E. Shilov. In particular, I'm interested in the results conerning the uniqueness classes (Chapter 2). It seems that such results are quite general and I'm trying to apply the same tools to the following:
\begin{cases} \partial_t v(t,x,y)\, = \, \partial_x^4v(t,x,y)+\partial_y^2v(t,x,y) \quad \text{on }\mathbb{R}^2_T;\\ v(0,x,y)=0 \quad \text{on }\mathbb{R}^2, \end{cases}
where $t \in [0,T]$. If I have undrstood the trick, the uniqueness class depends on reduced order $p$ of a system and it consists of the functions described by inequalities of the form \begin{equation} |v(x)|<k_1\cdot\exp[k_2\cdot|x|^p], \end{equation} with $k_1, k_2$ constants.
Now, it is not clear to me how these arguments could be applied to the problem above. Is simply $p=4$? Is there any reduction that I can't see? Are the two different derivatives (one with respect to $x$, one with respect to $y$) a problem?