Entire Solutions and Asymptotic Behavior to a Class of Parabolic $k$-Hessian Equations with More General Right-Hand Side Terms
Year: 2026
Type: preprint
Abstract: This paper investigates entire classical separable variable radial solutions to a class of parabolic k-Hessian equations -u_t (sigma_k(lambda(D^2u)))^alpha = f(|x|)g(t), where the right-hand side consists of positive continuous functions. Without assuming that -u_t is positively bounded, we extend previous work for the equations whose right-hand side is 1 to more general cases, including cases where the right-hand side terms are bounded and periodic. By employing the method of Euler's broken line, we obtain the existence and nonexistence results. Furthermore, we obtain the precise asymptotic power exponent.
Source: arXiv (Cornell University)
Authors: An, Ning, Bao, Jiguang
Institution: Beijing Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214349297