Space Analyticity for the Nonlinear Heat Equation in a Bounded Domain
نویسندگان
چکیده
In [FoT], Foias and Temam introduced a method for estimating the space-analyticity radius of solutions of the Navier Stokes equation with periodic boundary conditions. For the numerous applications, see e.g. [CEES, CRT, DTH, FT, Gr, K, LO]. In our previous paper [GK], we did not use the Fourier series and were thus able to treat the Navier Stokes and other semilinear parabolic equations with singular (L ) initial data. In particular, we expressed the analyticity radius in terms of the Reynolds number. Although it is well-known (cf. [M1, M2, G, HKR]) that solutions are analytic in the space variable also in the case of Dirichlet boundary conditions, it was not clear how to generalize the method of Foias and Temam to treat this case as well. The purpose of this paper is to show that this is indeed possible and illustrate the method on the non-linear heat equation. The main idea is to establish an energy inequality for the quantity
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