Boundary value problems for some classes of higher-order equations that are unsolved with respect to the highest derivative (Q1920696)

Of concern are differential equations of the form \[ \partial_t^{m+2}[A_m u]+\partial_t^{m+1}[B_m u]+\partial_t^{m}[C_m u]+ \sum_{j=1}^m \partial_t^{m-j}[A_{m-j} u]=f(t,\cdot) \] with \(A_j\), \(B_m\) and \(C_m\) differential operators of elliptic or elliptic-parabolic type. The author establishes existence and uniqueness in various settings including a so-called partially hyperbolic case. The results rely on coerciveness properties.