TY - JOUR
T1 - Complicated Asymptotic Behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation
AU - Wang , Liang-Wei
AU - Wang , Shu-Ying
AU - Yin , Jingxue
AU - Tu , Zheng-Wen
JO - Communications in Mathematical Research 
VL - 2
SP - 231
EP - 253
PY - 2023
DA - 2023/04
SN - 39
DO - http://doi.org/10.4208/cmr.2022-0050
UR - https://global-sci.org/intro/article_detail/cmr/21546.html
KW - Complexity, asymptotic behavior, doubly nonlinear diffusion equation.
AB - <p style="text-align: justify;">In this paper, we analyze the large time behavior of nonnegative solutions to the doubly nonlinear diffusion equation $$u_t−{\rm div}(|∇u^m|^{p−2}∇u^m)=0$$ in $\mathbb{R}^N$ with $p&gt;1,$ $m&gt;0$ and $m(p−1)−1&gt;0.$ By using the finite propagation property and the $L^1-L^∞$ smoothing effect, we find that the complicated asymptotic behavior of the rescaled solutions $t^{\mu/2}u(t^{β_·},t)$ for $0&lt;\mu&lt;2N/(N[m(p−1)−1]+p)$ and $β&gt;(2−\mu[m(p−1)−1])/(2p)$ can take place.</p>