Publication: Smoothing and perturbation for some fourth order linear parabolic equations in R-N
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We solve some fourth order parabolic equations, obtained from perturbations of the parabolic bi-Laplacian equation, with special focus on smoothing estimates. Several classes of initial data are considered including data in Lebesgue and Bessel-Lebesgue spaces. Robustness and convergence with respect to the perturbation are also obtained. Also, initial data in large uniform Bessel-Lebesgue spaces are considered as well as equations with higher order powers of the Laplacian.