The Stability of Small Stationary Solutions in Morrey Spaces of the Semilinear Heat Equations

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J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 4, Page 793--822.

Xiaofang, Zhou
The Stability of Small Stationary Solutions in Morrey Spaces of the Semilinear Heat Equations
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Abstract:
In this paper, we consider in Morrey spaces the Cauchy problem of the semilinear heat equation with an external force. Under appropriate assumptions on the external force, we proved the unique existence of small solution to the corresponding stationary problem. Moreover, if the initial data is close enough to the stationary solution, we verified the time-global solvability of the Cauchy problem, which leads to the stability of the small stationary solution.

Keywords: Morrey spaces, stability, semilinear heat equations, stationary solutions, semigroup operator

Mathematics Subject Classification (1991): Primary 35B35; Secondary 35K55

Mathematical Reviews Number: MR1742601

Received: 1998-11-18

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