Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data
In this article, we study the following noncoercive quasilinear parabolic problem ∂u∂t−diva(x,t,u,∇u)+ν∣u∣s−1u=λ∣u∣p−2u∣x∣p+finQT,u=0onΣT,u(x,0)=u0inΩ,\left\{\begin{array}{ll}\frac{\partial u}{\partial t}-\hspace{0.1em}\text{div}\hspace{0.1em}a\left(x,t,u,\nabla u)+\nu {| u| }^{s-1}u=\lambda \frac{{...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-06-01
|
| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/msds-2022-0168 |
| _version_ | 1797795037842505728 |
|---|---|
| author | Ahmedatt Taghi Hajji Youssef Hjiaj Hassane |
| author_facet | Ahmedatt Taghi Hajji Youssef Hjiaj Hassane |
| author_sort | Ahmedatt Taghi |
| collection | DOAJ |
| description | In this article, we study the following noncoercive quasilinear parabolic problem ∂u∂t−diva(x,t,u,∇u)+ν∣u∣s−1u=λ∣u∣p−2u∣x∣p+finQT,u=0onΣT,u(x,0)=u0inΩ,\left\{\begin{array}{ll}\frac{\partial u}{\partial t}-\hspace{0.1em}\text{div}\hspace{0.1em}a\left(x,t,u,\nabla u)+\nu {| u| }^{s-1}u=\lambda \frac{{| u| }^{p-2}u}{{| x| }^{p}}+f& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{Q}_{T},\\ u=0& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}{\Sigma }_{T},\\ u\left(x,0)={u}_{0}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\end{array}\right. with f∈L1(QT)f\in {L}^{1}\left({Q}_{T}) and u0∈L1(Ω){u}_{0}\in {L}^{1}\left(\Omega ) and show the existence of entropy solutions for this noncoercive parabolic problem with Hardy potential and L1-data. |
| first_indexed | 2024-03-13T03:11:50Z |
| format | Article |
| id | doaj.art-66cf5959782640bb8940f45c1c449dc0 |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-03-13T03:11:50Z |
| publishDate | 2023-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-66cf5959782640bb8940f45c1c449dc02023-06-26T10:46:54ZengDe GruyterNonautonomous Dynamical Systems2353-06262023-06-0110136237710.1515/msds-2022-0168Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-dataAhmedatt Taghi0Hajji Youssef1Hjiaj Hassane2Department of Mathematics and Computer Science, Laboratory G3A, Faculty of Sciences and Technology, University of Nouakchott, P. Box 880 Nouakchott, MauritaniaDepartment of Mathematics, Faculty of Sciences, University Abdelmalek Essaadi, BP 2121, Tetouan, MoroccoDepartment of Mathematics, Faculty of Sciences, University Abdelmalek Essaadi, BP 2121, Tetouan, MoroccoIn this article, we study the following noncoercive quasilinear parabolic problem ∂u∂t−diva(x,t,u,∇u)+ν∣u∣s−1u=λ∣u∣p−2u∣x∣p+finQT,u=0onΣT,u(x,0)=u0inΩ,\left\{\begin{array}{ll}\frac{\partial u}{\partial t}-\hspace{0.1em}\text{div}\hspace{0.1em}a\left(x,t,u,\nabla u)+\nu {| u| }^{s-1}u=\lambda \frac{{| u| }^{p-2}u}{{| x| }^{p}}+f& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{Q}_{T},\\ u=0& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}{\Sigma }_{T},\\ u\left(x,0)={u}_{0}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\end{array}\right. with f∈L1(QT)f\in {L}^{1}\left({Q}_{T}) and u0∈L1(Ω){u}_{0}\in {L}^{1}\left(\Omega ) and show the existence of entropy solutions for this noncoercive parabolic problem with Hardy potential and L1-data.https://doi.org/10.1515/msds-2022-0168quasilinear parabolic equationsnoncoercive equationshardy potentialentropy solutions35k1035k59 |
| spellingShingle | Ahmedatt Taghi Hajji Youssef Hjiaj Hassane Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data Nonautonomous Dynamical Systems quasilinear parabolic equations noncoercive equations hardy potential entropy solutions 35k10 35k59 |
| title | Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data |
| title_full | Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data |
| title_fullStr | Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data |
| title_full_unstemmed | Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data |
| title_short | Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data |
| title_sort | quasilinear class of noncoercive parabolic problems with hardy potential and l1 data |
| topic | quasilinear parabolic equations noncoercive equations hardy potential entropy solutions 35k10 35k59 |
| url | https://doi.org/10.1515/msds-2022-0168 |
| work_keys_str_mv | AT ahmedatttaghi quasilinearclassofnoncoerciveparabolicproblemswithhardypotentialandl1data AT hajjiyoussef quasilinearclassofnoncoerciveparabolicproblemswithhardypotentialandl1data AT hjiajhassane quasilinearclassofnoncoerciveparabolicproblemswithhardypotentialandl1data |