PreprintCC BY-NC-SA 4.0arXiv
Entire Solutions and Asymptotic Behavior to a Class of Parabolic k-Hessian Equations with More General Right-Hand Side Terms
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.
Related
- Existence and asymptotic behavior of radial solutions for a k-Hessian equation with the gradient
- Local behavior of solutions to inhomogeneous singular parabolic p-Laplace equations
- Asymptotic behavior of bounded Mild Solutions to some fractional differential equations involving the ψ-Hilfer derivative
- Global Well-Posedness and Large Time Asymptotic Behavior of Strong Solutions to the Compressible Viscous Non-Resistive MHD Equations with Vacuum
- Asymptotic behavior of solutions of the compressible MHD equations on the half space
BibTeX
@misc{an2026entire,
title = {{Entire Solutions and Asymptotic Behavior to a Class of Parabolic $k$-Hessian Equations with More General Right-Hand Side Terms}},
author = {Ning An and Jiguang Bao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29218},
eprint = {2609.29218},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29218},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Entire Solutions and Asymptotic Behavior to a Class of Parabolic k-Hessian Equations with More General Right-Hand Side Terms
AU - Ning An
AU - Jiguang Bao
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29218
UR - https://arxiv.org/abs/2609.29218
AB - 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.
ER -