Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term
| Autor: | Dao Nguyen Anh, Díaz Jesus Ildefonso, Nguyen Quan Ba Hong |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Advanced Nonlinear Studies, Vol 20, Iss 2, Pp 477-502 (2020) |
| Druh dokumentu: | article |
| ISSN: | 1536-1365 2169-0375 |
| DOI: | 10.1515/ans-2020-2076 |
| Popis: | We consider the high-dimensional equation ∂tu-Δum+u-βχ{u>0}=0{\partial_{t}u-\Delta u^{m}+u^{-\beta}{\chi_{\{u>0\}}}=0}, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution u∈𝒞([0,T];Lδ1(Ω)){u\in\mathcal{C}([0,T];L_{\delta}^{1}(\Omega))}, with u-βχ{u>0}∈L1((0,T)×Ω){u^{-\beta}\chi_{\{u>0\}}\in L^{1}((0,T)\times\Omega)}, δ(x)=d(x,∂Ω){\delta(x)=d(x,\partial\Omega)}, we prove some pointwise gradient estimates for a certain range of the dimension N, m≥1{m\geq 1} and β∈(0,m){\beta\in(0,m)}, mainly when the absorption dominates over the diffusion (1≤m |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|