Protter-Morawetz Problem for a Keldysh-Type Equation with Power-Type Degeneracy of Order m= 4/3

摘要

In series of our works ([6, 7, 18, 19]) we considered a four-dimensional Protter-Morawetz problem for a Keldysh-type weakly hyperbolic equation with power-type degeneracy of order m, where 0 < m < 2. It was shown that this problem is not well posed, since it has an infinite-dimensional cokernel, but it can be studied in the frame of generalized solutions with possible big singularities. However, existence and uniqueness results, as well as results on the asymptotic behavior of the singular solutions, were established only for the case 0 < m < 4/3. In this paper we succeed to extend these results for m= 4/3.