Abstract
We solve some linear parabolic equations obtained from perturbations of parabolic equations given by operators defining analytic semigroups. We consider several classes of initial data, in particular in low regularity spaces taken from the uniform Bessel-Lebesgue scale of spaces. We make special focus on smoothing estimates of the solution. Robustness and convergence with respect to the perturbation are also obtained.
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Notes
- 1.
Partially supported by Project MTM2012-31298, MICINN and GR58/08 Grupo 920894, UCM, Spain.
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Quesada, C., Rodríguez-Bernal, A. (2014). Perturbation of Analytic Semigroups in Uniform Spaces in \(\mathbb{R}^{N}\) . In: Casas, F., Martínez, V. (eds) Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-06953-1_5
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DOI: https://doi.org/10.1007/978-3-319-06953-1_5
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