Abstract
This article mainly consists of two parts. In the first part the initial value problem (IVP) of the semilinear heat equation
with initial data in\(\dot L_{r,p} \) is studied. We prove the well-posedness when
and construct non-unique solutions for
In the second part the well-posedness of the avove IVP for k=2 with μ0ɛH s(ℝn) is proved if
and this result is then extended for more general nonlinear terms and initial data. By taking special values of r, p, s, and u0, these well-posedness results reduce to some of those previously obtained by other authors [4, 14].
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Acknowledgements and Notes. This work is supported by NSF grant DMS 9304580 at IAS.
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Wu, J. Well-posedness of a semilinear heat equation with weak initial data. The Journal of Fourier Analysis and Applications 4, 629–642 (1998). https://doi.org/10.1007/BF02498228
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DOI: https://doi.org/10.1007/BF02498228