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Abstract and Applied Analysis
Volume 1 (1996), Issue 3, Pages 263-276

Global solutions of semilinear heat equations in Hilbert spaces

Department of Mathematics and Statistics, York Univeristy, 4700 Keele Street, North York, Ontario M3J1P3, Canada

Received 14 June 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one-parameter strongly continuous semigroups of bounded linear operators. Applications to special semilinear heat equations in L2(n) governed by pseudo-differential operators are given.