Uniqueness of the solution of nonlinear totally characteristic partial differential equations
-
- TAHARA Hidetoshi
- Department of Mathematics Sophia University
Search this article
Description
Let us consider the following nonlinear singular partial differential equation (t ∂/∂ t)^m u =F ( t, x, {(t ∂/∂ t)^j (∂/∂ x)α u }j+α ≤ m, j<m ) in the complex domain with two independent variables (t, x) ∈ \BC^2. When the equation is of totally characteristic type, this equation was solved in \cite{ct2} and \cite{resont} under certain Poincaré condition. In this paper, the author will prove the uniqueness of the solution under the assumption that u(t, x) is holomorphic in {(t, x) ∈ \BC^2 ; 0 < |t|<r, | \arg t| < θ, |x|<R} for some r>0, θ >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.
Journal
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 57 (4), 1045-1065, 2005
The Mathematical Society of Japan
- Tweet
Details 詳細情報について
-
- CRID
- 1390001205115187328
-
- NII Article ID
- 10017178079
-
- NII Book ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- MRID
- 2183583
-
- NDL BIB ID
- 7493097
-
- Text Lang
- en
-
- Data Source
-
- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
-
- Abstract License Flag
- Disallowed