Litovchenko, V. A. The Cauchy problem for one class of parabolic pseudodifferential systems with nonsmooth symbols. (Russian, English) Zbl 1164.35538 Sib. Mat. Zh. 49, No. 2, 374-393 (2008); translation in Sib. Math. J. 49, No. 2, 300-316 (2008). Summary: In the class of finite-order distributions we establish the well-posedness of the Cauchy problem for parabolic pseudodifferential systems whose symbols are nonsmooth functions at a fixed point \(h\in\mathbb R^n\) generated by homogeneous functions of order \(\gamma >0\) depending on time. Cited in 4 Documents MSC: 35S10 Initial value problems for PDEs with pseudodifferential operators Keywords:Cauchy problem; pseudodifferential system; nonsmooth symbol; convolution; distribution; matriciant PDFBibTeX XMLCite \textit{V. A. Litovchenko}, Sib. Mat. Zh. 49, No. 2, 375--394 (2008; Zbl 1164.35538); translation in Sib. Math. J. 49, No. 2, 300--316 (2008) Full Text: EuDML EMIS