×

zbMATH — the first resource for mathematics

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)
MSC:
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
PDF BibTeX XML Cite