First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients
For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,...
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/1019038 |
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| author | Aziz Harman Ezgi Harman |
| author_facet | Aziz Harman Ezgi Harman |
| author_sort | Aziz Harman |
| collection | DOAJ |
| description | For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n−1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n−1,n≥2. |
| format | Article |
| id | doaj-art-a806efb6cd51401aaf0a96a58d9d8012 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a806efb6cd51401aaf0a96a58d9d80122025-02-03T01:04:08ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/10190381019038First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous CoefficientsAziz Harman0Ezgi Harman1Department of Mathematics, Science and Arts Faculty Batman University, Batman, TurkeyDepartment of Mathematics, Science and Arts Faculty Batman University, Batman, TurkeyFor a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n−1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n−1,n≥2.http://dx.doi.org/10.1155/2020/1019038 |
| spellingShingle | Aziz Harman Ezgi Harman First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients Journal of Mathematics |
| title | First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients |
| title_full | First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients |
| title_fullStr | First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients |
| title_full_unstemmed | First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients |
| title_short | First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients |
| title_sort | first boundary value problem for cordes type semilinear parabolic equation with discontinuous coefficients |
| url | http://dx.doi.org/10.1155/2020/1019038 |
| work_keys_str_mv | AT azizharman firstboundaryvalueproblemforcordestypesemilinearparabolicequationwithdiscontinuouscoefficients AT ezgiharman firstboundaryvalueproblemforcordestypesemilinearparabolicequationwithdiscontinuouscoefficients |