Rodríguez Bernal, AníbalCholewa, Jan W.2023-06-202023-06-202010-010362-546X10.1016/j.na.2011.08.022https://hdl.handle.net/20.500.14352/42474In 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0362546X1100575Xhttp://www.sciencedirect.com/restricted access517.986Interpolation spacesFractional powers of operatorsAnalytic semigroupsInitial value problems for higher order parabolic equationsSemilinear parabolic equationsCritical exponentsCritical NonlinearitiesFunciones (Matemáticas)1202 Análisis y Análisis Funcional