%0 Journal Article
%A Rodríguez Bernal, Aníbal
%A Cholewa, Jan W.
%T Linear and semilinear higher order parabolic equations in R-N
%D 2010
%@ 0362-546X
%U https://hdl.handle.net/20.500.14352/42474
%X In this paper we consider some fourth order linear and semilinear equations in R-N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1 < p < infinity prove that for a suitable family of Bessel potential spaces, H-p(alpha) (R-N), the linear equation defines a strongly continuous analytic semigroup.Using this result, we prove that the nonlinear problems we consider can be solved for initial data in L-p(RN) and in H-p(2) (R-N). We also find the corresponding critical exponents, that is, the largest growth allowed for the nonlinear terms for these classes of initial data.
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