当前位置: X-MOL 学术J. Differ. Equ. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On the local existence for a weakly parabolic system in Lebesgue spaces
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2020-03-01 , DOI: 10.1016/j.jde.2019.09.049
Aldryn Aparcana , Ricardo Castillo , Omar Guzmán-Rea , Miguel Loayza

Abstract We consider the parabolic system u t − a Δ u = f ( v ) , v t − b Δ v = g ( u ) in Ω × ( 0 , T ) , where a , b > 0 , f , g : [ 0 , ∞ ) → [ 0 , ∞ ) are non-decreasing continuous functions and either Ω is a bounded domain with smooth boundary ∂Ω or the whole space R N . We characterize the functions f and g so that the system has a local solution for every initial data ( u 0 , v 0 ) ∈ L r ( Ω ) × L s ( Ω ) , u 0 , v 0 ≥ 0 , r , s ∈ [ 1 , ∞ ) .

中文翻译:

勒贝格空间弱抛物线系统的局部存在性

摘要 我们考虑抛物线系统 ut − a Δ u = f ( v ) , vt − b Δ v = g ( u ) in Ω × ( 0 , T ) ,其中 a , b > 0 , f , g : [ 0 , ∞ ) → [ 0 , ∞ ) 是非递减连续函数,Ω 是具有平滑边界 ∂Ω 的有界域或整个空间 RN 。我们对函数 f 和 g 进行表征,以便系统对每个初始数据 (u 0 , v 0 ) ∈ L r ( Ω ) × L s ( Ω ) , u 0 , v 0 ≥ 0 , r , s 都有一个局部解∈ [ 1 , ∞ ) 。
更新日期:2020-03-01
down
wechat
bug