| Abstract: |
| In this talk, we make a systematic investigation of the existence, uniqueness and nonexistence of entire separable variable radial solutions to the following class of parabolic k-Hessian equations with the parameter:
$$
-u_t [S_k(D^2u)]^{\alpha}=1
$$
We also study the asymptotic behavior and its refined version of the solution at infinity. We particularly note that our results fully generalize the result of An, Bao, et al. in Nonlinear Anal. 239:113441 (2024) for the parabolic Monge-Amp{\`e}re equation in the form of $-u_t \det D^2u=1$. The main tools employed in this work comprise Euler`s broken line method, local boundedness estimate, Keller-Osserman type criteria, the generalized L`Hospital`s rule, and asymptotic stability analysis. |
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