Existence of a Renormalized Solution for a Class of Parabolic Problems
In the paper, we prove the existence of the renormalized solution for the nonlinear degenerate parabolic equation $\frac{\partial b(u)}{\partial t}-\textrm{div}(A(t,x,u)Du)=f,$ where the matrix $A\left( t,x,s\right) =\left(a_{ij}(t,x,s)\right)_{1\leq i\leq N \atop 1\leq j\leq N}$ is not controlled w...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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oai:jmag.ilt.kharkiv.ua:article-11072025-12-08T18:45:45Z Existence of a Renormalized Solution for a Class of Parabolic Problems Existence of a Renormalized Solution for a Class of Parabolic Problems Existence of a Renormalized Solution for a Class of Parabolic Problems El Fatry, Mohammed Mekkour, Mounir Akdim, Youssef ренормалізований розв'язок вибух $L^{1}$-дані renormalized solutions blow-up $L^{1}$-data In the paper, we prove the existence of the renormalized solution for the nonlinear degenerate parabolic equation $\frac{\partial b(u)}{\partial t}-\textrm{div}(A(t,x,u)Du)=f,$ where the matrix $A\left( t,x,s\right) =\left(a_{ij}(t,x,s)\right)_{1\leq i\leq N \atop 1\leq j\leq N}$ is not controlled with respect to $u$, $f\in L^{1}(Q) $, and $b$ is a strictly increasing $C^{1}$-function. Mathematical Subject Classification 2020: 47A15, 46A32 У цій статті ми доводимо існування ренормалізованого розв'язку для нелінійного виродженого параболічного рівняння $\frac{\partial b(u)}{\partial t}-\textrm{div}(A(t,x,u)Du)=f,$ де матриця $A\left( t,x,s\right) =\left(a_{ij}(t,x,s)\right)_{1\leq i\leq N \atop 1\leq j\leq N}$ не контролюється за $u$, $f\in L^{1}(Q) $, а $b$ є строго зростальною $C^{1}$-функцією. Mathematical Subject Classification 2020: 47A15, 46A32 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2025-07-18 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1107 10.15407/mag21.03.04 Journal of Mathematical Physics, Analysis, Geometry; Vol. 21 No. 3 (2025); 302–318 Журнал математической физики, анализа, геометрии; Том 21 № 3 (2025); 302–318 Журнал математичної фізики, аналізу, геометрії; Том 21 № 3 (2025); 302–318 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1107/jm21-0302e |
| institution |
Journal of Mathematical Physics, Analysis, Geometry |
| baseUrl_str |
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| datestamp_date |
2025-12-08T18:45:45Z |
| collection |
OJS |
| language |
English |
| topic |
ренормалізований розв'язок вибух $L^{1}$-дані |
| spellingShingle |
ренормалізований розв'язок вибух $L^{1}$-дані El Fatry, Mohammed Mekkour, Mounir Akdim, Youssef Existence of a Renormalized Solution for a Class of Parabolic Problems |
| topic_facet |
ренормалізований розв'язок вибух $L^{1}$-дані renormalized solutions blow-up $L^{1}$-data |
| format |
Article |
| author |
El Fatry, Mohammed Mekkour, Mounir Akdim, Youssef |
| author_facet |
El Fatry, Mohammed Mekkour, Mounir Akdim, Youssef |
| author_sort |
El Fatry, Mohammed |
| title |
Existence of a Renormalized Solution for a Class of Parabolic Problems |
| title_short |
Existence of a Renormalized Solution for a Class of Parabolic Problems |
| title_full |
Existence of a Renormalized Solution for a Class of Parabolic Problems |
| title_fullStr |
Existence of a Renormalized Solution for a Class of Parabolic Problems |
| title_full_unstemmed |
Existence of a Renormalized Solution for a Class of Parabolic Problems |
| title_sort |
existence of a renormalized solution for a class of parabolic problems |
| title_alt |
Existence of a Renormalized Solution for a Class of Parabolic Problems Existence of a Renormalized Solution for a Class of Parabolic Problems |
| description |
In the paper, we prove the existence of the renormalized solution for the nonlinear degenerate parabolic equation $\frac{\partial b(u)}{\partial t}-\textrm{div}(A(t,x,u)Du)=f,$ where the matrix $A\left( t,x,s\right) =\left(a_{ij}(t,x,s)\right)_{1\leq i\leq N \atop 1\leq j\leq N}$ is not controlled with respect to $u$, $f\in L^{1}(Q) $, and $b$ is a strictly increasing $C^{1}$-function.
Mathematical Subject Classification 2020: 47A15, 46A32 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2025 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1107 |
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AT elfatrymohammed existenceofarenormalizedsolutionforaclassofparabolicproblems AT mekkourmounir existenceofarenormalizedsolutionforaclassofparabolicproblems AT akdimyoussef existenceofarenormalizedsolutionforaclassofparabolicproblems |
| first_indexed |
2025-09-27T01:57:16Z |
| last_indexed |
2025-12-17T12:06:07Z |
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1851757080491327488 |