Cauchy problem for parabolic systems with convolution operators in periodic spaces (Q941912)

The author gives a detailed presentation of the Gevrey functions and the Gevrey ultradistributions on the \(n\)-torus \(\mathbb{T}^n\). In this frame, the author then considers the Cauchy problem: \(\partial_t u= Au\), \(u(0)= f\), where \(A\) is a matrix of convolution operators on \(\mathbb{T}\), satisfying standard parabolicity conditions. Relevant examples for \(A\) are operators involving fractional derivatives. Precise well-posedness results are obtained for Gevrey data \(f\) and Gevrey solutions \(u\).