Pseudodifferential multi-product representation of the solution operator of a parabolic equation

Details Pseudodifferential multi-product representation of the solution operator of a parabolic equation Pseudodifferential multi-product representation of the solution operator of a parabolic equation

2008-01-24

arxiv.org/abs/0801.3838v2

Comm. Partial Differential Equations 34, 7 (2009) 625 - 655

Mathematics

Analysis of PDEs

Comm. Partial Differential Equations to appear (2009) 28 pages

Scientific paper

10.1080/03605300903017330

By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on $\R^n$ as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof is based on an effective use of the Weyl calculus and the Fefferman-Phong inequality.

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