Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data
We study the quasilinear elliptic system $$ -mathop{ m div}sigma(x,u,Du) =v(x)+f(x,u)+mathop{ m div}g(x,u) $$ on a bounded domain of $mathbb{R}^n$ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source $v$ in a moving and dissolving substance,...
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| Format: | Article |
| Language: | English |
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Texas State University
2004-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/144/abstr.html |
| _version_ | 1819175435440750592 |
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| author | Fabien Augsburger Norbert Hungerbuehler |
| author_facet | Fabien Augsburger Norbert Hungerbuehler |
| author_sort | Fabien Augsburger |
| collection | DOAJ |
| description | We study the quasilinear elliptic system $$ -mathop{ m div}sigma(x,u,Du) =v(x)+f(x,u)+mathop{ m div}g(x,u) $$ on a bounded domain of $mathbb{R}^n$ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source $v$ in a moving and dissolving substance, where the motion is described by $g$ and the dissolution by $f$. We prove existence of a weak solution of this system under classical regularity, growth, and coercivity conditions for $sigma$, but with only very mild monotonicity assumptions. |
| first_indexed | 2024-12-22T20:54:49Z |
| format | Article |
| id | doaj.art-272cc08243f846898bab557048b26000 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T20:54:49Z |
| publishDate | 2004-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-272cc08243f846898bab557048b260002022-12-21T18:12:59ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-12-012004144118Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical dataFabien AugsburgerNorbert HungerbuehlerWe study the quasilinear elliptic system $$ -mathop{ m div}sigma(x,u,Du) =v(x)+f(x,u)+mathop{ m div}g(x,u) $$ on a bounded domain of $mathbb{R}^n$ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source $v$ in a moving and dissolving substance, where the motion is described by $g$ and the dissolution by $f$. We prove existence of a weak solution of this system under classical regularity, growth, and coercivity conditions for $sigma$, but with only very mild monotonicity assumptions.http://ejde.math.txstate.edu/Volumes/2004/144/abstr.htmlYoung measurenoninear elliptic systems. |
| spellingShingle | Fabien Augsburger Norbert Hungerbuehler Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data Electronic Journal of Differential Equations Young measure noninear elliptic systems. |
| title | Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data |
| title_full | Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data |
| title_fullStr | Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data |
| title_full_unstemmed | Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data |
| title_short | Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data |
| title_sort | quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data |
| topic | Young measure noninear elliptic systems. |
| url | http://ejde.math.txstate.edu/Volumes/2004/144/abstr.html |
| work_keys_str_mv | AT fabienaugsburger quasilinearellipticsystemsindivergenceformwithweakmonotonicityandnonlinearphysicaldata AT norberthungerbuehler quasilinearellipticsystemsindivergenceformwithweakmonotonicityandnonlinearphysicaldata |