Global version of the Cauchy-Kovalevskaia theorem for nonlinear PDEs (Q810258)

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 \[ D_ t^ mU(t,y)=G(t,y,...,D_ t^ pD^ q_ yU,...),\quad y\in {\mathbb{R}}^{n-1}, \] \(0\leq p<m\), q a multi-index with \(p+| q| \leq m\), which satisfy the noncharacteristic Cauchy data \[ D_ t^ pU(t_ 0,y)=g_ p(y),\quad 0\leq p<m. \] 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.