2026-06-27T01:07:28Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/335772023-08-26T03:53:45Zcom_20.500.14352_14col_20.500.14352_15

Cholewa, Jan W. Rodríguez Bernal, Aníbal 2023-06-19T13:24:30Z 2023-06-19T13:24:30Z 2014-07 0362-546X 10.1016/j.na.2014.03.013 https://hdl.handle.net/20.500.14352/33577 http://www.sciencedirect.com/science/article/pii/S0362546X14001072 http://www.elsevier.com Due to the lack of the maximum principle the analysis of higher order parabolic problems in RN is still not as complete as the one of the second-order reaction-diffusion equations. While the critical exponents and then a dissipative mechanism in the subcritical case have already been satisfactorily described (see Cholewa and Rodriguez-Bernal (2012)), for problems in the critical or supercritical regime the questions concerning well or illposedness, as well as possible dissipative properties of the solutions, have not yet been satisfactorily answered. This article is devoted to the analysis of the higher order parabolic problems in R-N in the latter case. Focusing on the critical and supercritical regimes we give sufficient "good"-sign conditions proving that the problem is then globally well posed in L-2(R-N) and even possesses a compact global attractor. On the other hand, for supercritically growing "bad"-signed nonlinearities we show that the problem is ill-posed. eng restricted access Critical and supercritical higher order parabolic problems in R-N journal article