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An integral formula for multidimensional evolution equations

Author: E. C. Svendsen
Journal: Proc. Amer. Math. Soc. 92 (1984), 385-390
MSC: Primary 47D05; Secondary 35K22
MathSciNet review: 759658
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Abstract: This paper contains an integral formula for the one-parameter semigroup generated by a sum of contractions of operator-valued tensors. The formula expresses the semigroup in terms of the semigroups generated by the quadratic forms associated with the tensors. It is used to construct solutions of some wave and diffusion equations from solutions of related lower-dimensional equations.

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