Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4672807 | Indagationes Mathematicae | 2015 | 18 Pages |
Abstract
If Ω is an open bounded set in RN, Nâ¥2, with a connected Lipschitz boundary âΩ, a(x,ξ) is an operator of Leray-Lions type, β and γ are non decreasing continuous real functions, β(0)=γ(0)=0, then for every (f,g)âL1(]0,T[ÃRN)ÃL1(]0,T[ÃâΩ),(u0,v0)âL1(RN)ÃL1(âΩ), we prove that the entropy solution coincides with the renormalized solution to the following problem: {uâ²âdiv[a(.,âu)]+β(u)=fon ]0,T[Ã(RNââΩ),(Ïu)â²+[âuâνa]+γ(Ïu)=g  and [u]=0on ]0,T[ÃâΩ,(u(0,.),Ïu(0,.))=(u0,v0)a.e. on RNÃâΩ, where [u] and [âuâνa] are respectively the jump across âΩ of u and the normal derivative âuâνa related to the operator a.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Chiraz Kouraichi, Abdelmajid Siai,