Ultraparabolic equations. (English. Russian original) Zbl 0128.32503

Genchev, T. G.

Sov. Math., Dokl. 4, 979-982 (1963); translation from Dokl. Akad. Nauk SSSR 151, 265-268 (1963).

Equations of the type \[ \sum_{i,j=1}^n a_{ij}\frac{\partial^2u}{\partial x_i\partial x_j}+\sum_{i=1}^n b_i\frac{\partial u}{\partial x_i}=a_0\frac{\partial u}{\partial t}+\sum_{k=1}^m b_i\frac{\partial u}{\partial y_k}+bu+f \] are considered with \(\sum a_{ij}(x,y,t)\,\xi_i\,\xi_j\geq\mu\sum\xi_i^2\) and \(a_0(x,y,t)>\lambda>0\). Existence and uniqueness theorems for boundary value and Cauchy problems are stated.

Reviewer: R. Carroll

MSC:

35K70

Ultraparabolic equations, pseudoparabolic equations, etc.

Keywords:

Ultraparabolic equations; existence; uniqueness boundary value problem; Cauchy problem