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Zbl 0733.35002
Rosinger, Elemer E.
Global version of the Cauchy-Kovalevskaia theorem for nonlinear PDEs.
(English)
[J] Acta Appl. Math. 21, No.3, 331-343 (1990). ISSN 0167-8019; ISSN 1572-9036/e

The main result of this paper is the proof of the following result. There exist generalized solutions to the n-th order, nonlinear, analytic differential equation $$D\sb t\sp mU(t,y)=G(t,y,...,D\sb t\sp pD\sp q\sb yU,...),\quad y\in {\bbfR}\sp{n-1},$$ $0\le p<m$, q a multi-index with $p+\vert q\vert \le m$, which satisfy the noncharacteristic Cauchy data $$D\sb t\sp pU(t\sb 0,y)=g\sb p(y),\quad 0\le p<m.$$ The result is global and relies on previous work of the author and others on the nonlinear theory of generalized functions. The paper is very elegant but it is quite difficult as well.
[R.Guenther (Corvallis)]
MSC 2000:
*35A10 Cauchy-Kowalewski theorems
35D05 Existence of generalized solutions of PDE
35G25 Initial value problems for nonlinear higher-order PDE

Keywords: global solutions; analytic differential equation; noncharacteristic Cauchy data; generalized functions

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