Exact solutions of the inhomogeneous problems for polyparabolic operator (Q2711744)

The authors consider the equation NEWLINE\[NEWLINE T^{m+1}u\equiv \sum\limits_{j=0}^{m+1}(- 1)^j\binom{m+1}{j}\frac{\partial^{m-j+1}} {\partial t^{m- j+1}} \nabla^{2j}u(t,x)=f(t,x),\quad t>0, x\in \mathbb R^n. \tag{1} NEWLINE\]NEWLINE It is shown that in order to obtain a well-posed problem for the equation (1) the initial data NEWLINE\[NEWLINE (T^ku)(+0,x),\quad k=1,\ldots ,m, NEWLINE\]NEWLINE can be used. A fundamental solution is found explicitly.NEWLINENEWLINEFor the entire collection see [Zbl 0937.00046].