On the singular solutions of nonlinear singular partial differential equations I

TAHARA, Hidetoshi

J. Math. Soc. Japan, Tome 53 (2001) no. 3, p. 711-729 / Harvested from Project Euclid

Résumé

Let us consider the following nonlinear singular partial differential equation: $(t\partial_{t})^{m}u=F(t,x,\{(t\partial_{t})^{j}\partial_{x}^{\alpha}u\}_{j+|\alpha|\leq m,j0$ . Clearly $\mathscr{S}_{log}\supset \mathscr{S}_{+}$ . The paper gives a sufficient condition for $\mathscr{S}_{log}=\mathscr{S}_{+}$ to be valid.

Publié le : 2001-07-15
Classification: Nonlinear PDE, singular solutions, 35A20, 35B40

@article{1213023731,
     author = {TAHARA, Hidetoshi},
     title = {On the singular solutions of nonlinear singular partial differential equations I},
     journal = {J. Math. Soc. Japan},
     volume = {53},
     number = {3},
     year = {2001},
     pages = { 711-729},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1213023731}
}

TAHARA, Hidetoshi. On the singular solutions of nonlinear singular partial differential equations I. J. Math. Soc. Japan, Tome 53 (2001) no. 3, pp.  711-729. http://gdmltest.u-ga.fr/item/1213023731/