Singular Cauchy problem for a certain linear and 2nd order equation
Urabe, Jiichiroh
J. Math. Kyoto Univ., Tome 39 (1999) no. 4, p. 1-24 / Harvested from Project Euclid
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In this paper we consider the structure, in particular the singularities, of solutions of singular Cauchy problem for the following operator $L$ with holomorphic coefficients in the neighbourhood of the origin of $C^{2}$ under some conditions \[ L = D_{t}^{2} - (x +bt^{2})D_{x}^{2} - a(t, x)D_{t} - c(t, x)D_{x} - d (t , x). \] We construct its solution by so-called asymptotic expansion method and study its structure by the monodromy theory of the hypergeometric function.
Publié le : 1999-05-15
Classification:  35A20,  35C20 
@article{1250517951,
     author = {Urabe, Jiichiroh},
     title = {Singular Cauchy problem for a certain linear and 2nd order equation},
     journal = {J. Math. Kyoto Univ.},
     volume = {39},
     number = {4},
     year = {1999},
     pages = { 1-24},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250517951}
}

Urabe, Jiichiroh. Singular Cauchy problem for a certain linear and 2nd order equation. J. Math. Kyoto Univ., Tome 39 (1999) no. 4, pp.  1-24. http://gdmltest.u-ga.fr/item/1250517951/