Tricomi problem for a mixed parabolic-hyperbolic equation in a rectangular domain
The author considers the equation of mixed parabolic-hyperbolic type with one spatial variable in the rectangular domain. The type changes at a certain time simultaneously in all points. The conjugation condition holds at a line where the type changes. The Tricomi problem (kind of a Dirichlet problem) with zero boundary conditions is posed in the rectangular (i.e. on the spatial segment during finite time). Using the spectral analysis, the author establishes an existence and uniqueness criterion for the solution to the problem. The case of infinite time is considered.
scientific article; zbMATH DE number 5621821
scientific article