@Article{CMR-39-231,
author = {Wang , Liang-WeiWang , Shu-YingYin , Jingxue and Tu , Zheng-Wen},
title = {Complicated Asymptotic Behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation},
journal = {Communications in Mathematical Research },
year = {2023},
volume = {39},
number = {2},
pages = {231--253},
abstract = {
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 $p>1,$ $m>0$ and $m(p−1)−1>0.$ 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 $0<\mu<2N/(N[m(p−1)−1]+p)$ and $β>(2−\mu[m(p−1)−1])/(2p)$ can take place.
},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2022-0050},
url = {http://global-sci.org/intro/article_detail/cmr/21546.html}
}
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 -
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 $p>1,$ $m>0$ and $m(p−1)−1>0.$ 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 $0<\mu<2N/(N[m(p−1)−1]+p)$ and $β>(2−\mu[m(p−1)−1])/(2p)$ can take place.
Wang , Liang-WeiWang , Shu-YingYin , Jingxue and Tu , Zheng-Wen. (2023). Complicated Asymptotic Behavior of Solutions for the Cauchy Problem of Doubly Nonlinear Diffusion Equation.
Communications in Mathematical Research . 39 (2).
231-253.
doi:10.4208/cmr.2022-0050
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