Poisson operators for boundary problems concerning a class of degenerate parabolic equations (Q5949427)

Using the formal series method, the authors construct a Poisson operator for classical boundary problems concerning a class of degenerate parabolic equations: \(LU=\partial_t U-\partial^2_y U-y^2 \sum^n_{i,j =1} a_{ij}(t,x) \partial_{x_i}U \partial_{x_j} U+yb(t,x) \partial_y U+\sum^n_{i =1} a_i(t,x)\partial_{x_i} U+c(t,x)U= 0\), where the term \(\sum^n_{i,j=1} a_{ij} (t,x) \xi_i\xi_j\) is semi-definite positive, while \(\sum^n_{i,j=1} a_{ij} (0,x) \xi_i \xi_j\) is definite positive.