ncts

We construct global asymptotically self-similar solutions to the Hardy-H'enon parabolic equation or a large class of initial data belonging to weighted Lorentz spaces. The solution may be asymptotic to a self-similar solution of the linear heat equation or to a self-similar solution to the Hardy-H'enon equation depending on the decay of the initial data at infinity. The asymptotic results are new for the H’enon case. Furthermore, for complex-valued initial data, a more intricate asymptotic behaviors is shown; if either one of the real part or the imaginary part of the initial data has a spatial decay faster than the critical decay, then the solution exhibits a combined Nonlinear-``Modified Linear" asymptotic behavior, which is new even for the Fujita case. This talk is based on arXiv:2503.12408, a joint work with M. Ikeda (RIKEN), K. Taniguchi (Shizuoka U.) and S. Tayachi (University of Tunis El Manar).