Uniqueness of the solution of nonlinear totally characteristic partial differential equations

TAHARA, Hidetoshi

J. Math. Soc. Japan, Tome 57 (2005) no. 4, p. 1045-1065 / Harvested from Project Euclid

Résumé

Let us consider the following nonlinear singular partial differential equation $(t \partial/\partial t)^m u = F ( t,x, \{(t \partial/\partial t)^j (\partial/\partial x)^{\alpha} u \}_{j+\alpha \leq m, j0$ , $\theta >0$ , $R>0$ and that it satisfies $u(t,x) = O(|t|^a )$ (as $t \longrightarrow 0$ ) uniformly in $x$ for some $a>0$ . The result is applied to the problem of removable singularities of the solution.

Publié le : 2005-10-14
Classification: uniqueness of the solution, nonlinear PDE, totally characteristic PDE, 35A20, 35A10, 35G20

@article{1150287303,
     author = {TAHARA, Hidetoshi},
     title = {Uniqueness of the solution of nonlinear totally characteristic partial differential equations},
     journal = {J. Math. Soc. Japan},
     volume = {57},
     number = {4},
     year = {2005},
     pages = { 1045-1065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1150287303}
}

TAHARA, Hidetoshi. Uniqueness of the solution of nonlinear totally characteristic partial differential equations. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp.  1045-1065. http://gdmltest.u-ga.fr/item/1150287303/