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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.

MSC:

35S10 Initial value problems for PDEs with pseudodifferential operators
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