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Asymptotic expansions “in the large” of solutions of the complex Cauchy problem with singular initial data. (English. Russian original) Zbl 0798.58076
Sov. Math., Dokl. 44, No. 3, 674-677 (1992); translation from Dokl. Akad. Nauk SSSR 321, No. 2, 250-253 (1991).
The authors state without proof three theorems on the asymptotic behaviour in the large for the solution of the Cauchy problem \[ (-1)^ m {\partial^ m u\over \partial t^ m} - H(x,-{\partial\over \partial x})u = 0,\quad (-1)^ j {\partial^ j u\over \partial t^ j} = v_ j,\quad 0 \leq j \leq m - 1, \] where \(v_ j\) may have singularities.
Reviewer: N.Jacob (Erlangen)
58J47 Propagation of singularities; initial value problems on manifolds
58J37 Perturbations of PDEs on manifolds; asymptotics
35G10 Initial value problems for linear higher-order PDEs