Stability estimates for the solutions of a certain ultraparabolic equation
The paper deals with the ultraparabolic equation \(\partial_ 1u=\sum^{n}_{j=1}u_{x_ jx_ j},\) where \[ \partial_ 1u=\sum^{m}_{j=1}u_{t_ j}+\sum^{p}_{j=1}u_{\tau_ j},\quad X_ j>0,\quad t_ j>0,\quad \tau \in {\mathbb{R}}^ p. \] The stability estimations for solutions with the conditions \[ u|_{t_ j=0}=0,\quad u|_{x_ j=a_ j}=f(x,t,\tau),\quad j=1,...,n,\quad a_ j\geq 0,\quad \sum^{n}_{j=1}a_ j>0 \] are established.
scientific article; zbMATH DE number 4099793