On the existence of solution of a system of partial differential equations
Summary: Let \(\Pi_ \alpha= \{t\mid 0<\arg t<\alpha\}\) for \(\alpha<\pi\) and denote by \(M\) the class of \(m\)-dimensional vector functions \(u= u(x,t)\) of \(C^ \infty (\mathbb{R}^ n\times \overline{\Pi}_ \alpha)\) analytic in \(t\in \Pi_ \alpha\) and having polynomial growth in \((x,t)\). Let \(A(\xi)\) \((\xi\in \mathbb{R}^ n)\) be a square matrix of order \(m\) with polynomial elements. In the paper we define regularity and strict regularity of the system \(\partial u/\partial t= A(D_ x) u+f\) and prove its solvability in \(M\) for all \(f\in M\).
scientific article; zbMATH DE number 704301