Alves, Claudianor O.Boudjeriou, TahirPrado, Humberto2024-10-232024-10-2320240022-0396https://www.sciencedirect.com/science/article/abs/pii/S0022039624002456?via%3Dihubhttps://doi.org/10.1016/j.jde.2024.04.019https://dspace.univ-boumerdes.dz/handle/123456789/14512The objective of this paper is to investigate the existence of solutions and their qualitative behavior for a given class of nonlinear evolutionary equations. We demonstrate that the pseudo-differential operator Δexp⁡(−cΔ) acts as the infinitesimal generator of the solution operator. Here, Δ denotes the Euclidean Laplace operator, and c is a positive constant. We establish the appropriate domain for the operator Δexp⁡(−cΔ) and prove that it generates a C0 semigroup on L2(RN). Additionally, we introduce a scale of spaces wherein smooth solutions exist, and these spaces are continuously embedded into the Sobolev class. Finally, we investigate the nonlinear evolution problem for a broad class of nonlinearities.enAsymptotic behavior of solutionsBlowing up solutionsBosonic heat equationsGlobal existenceArticle