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- W34540035 abstract "A. Friedman [5] has generalized the classical theorems of Phragm’en-Lindelof type for the parabolic equations. In this paper we discuss some theorems of Phragm’en-Lindelof type for the heat equation on manifolds with “ nice “ properties and their appIications to the solutions of the heat equation. In S 2, we suppose that $M$ is a complete -Riemannian manifold with Ricci curvature bounded from below. Then we have a similar theorem for the heat operator as in Theorem 7 in [5] and may apply it to prove the uniqueness of the solutions with Cauchy data which are not necessarily bounded. Our result is an extension of the theorem in [3] which gives the uniqueness of bounded solutions. In S 3, we suppose that $M$ is a “ model “ with Ricci curvature bounded from below. Then we have a similar theorem for the heat equation as in Theorem 8 in [5] and that the solution with Cauchy data vanishing at infinity vanishes uniformly as time tends to infinity. In S 4, we apply theorems in S 3 to differential forms." @default.
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- W34540035 date "1983-01-01" @default.
- W34540035 modified "2023-09-24" @default.
- W34540035 title "SOME THEOREMS OF PHRAGMEN-LINDELOF TYPE FOR THE HEAT OPERATOR ON A CERTAIN MANIFOLD" @default.
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