Geodesic
Existence result for nonlinear parabolic problems with $L^1$-data
Abderrahmane El Hachimi1 ; Jaouad Igbida2 ; Ahmed Jamea1
1UFR Mathématiques Appliquées et Industrielles Faculté des Sciences B.P. 20, El Jadida, Morocco
2UFR Mathématiques Appliquées et Industrielles Faculté des Sciences B.P. 20, El Jadida, Marocco
Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 483-508
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the existence of solutions of the nonlinear parabolic problem$$\displaylines{ \frac{\partial u}{\partial t}-\mathop{ \rm div}[|Du-{\mit\Theta}(u)|^{p-2}(Du- {\mit\Theta}(u))] +\alpha(u)=f \quad\ \hbox{in } \mathopen{]}0, T\mathclose{[}\times{\mit\Omega},\cr (|Du-{\mit\Theta}(u)|^{p-2}(Du-{\mit\Theta}(u)))\cdot \eta + \gamma(u)=g \quad\ \hbox{on } \mathopen{]}0, T\mathclose{[}\times\partial{\mit\Omega}, \cr u(0,\cdot )=u_0 \quad\ \hbox{in } {\mit\Omega},\cr} $$ with initial data in $L^1$. We use a time discretization of the continuous problem by the Euler forward scheme.
DOI : 10.4064/am37-4-6
Keywords: study existence solutions nonlinear parabolic problem displaylines frac partial partial mathop div du mit theta p du mit theta alpha quad hbox mathopen mathclose times mit omega du mit theta p du mit theta cdot eta gamma quad hbox mathopen mathclose times partial mit omega cdot quad hbox mit omega initial time discretization continuous problem euler forward scheme

Abderrahmane El Hachimi  1   ; Jaouad Igbida  2   ; Ahmed Jamea  1

1 UFR Mathématiques Appliquées et Industrielles Faculté des Sciences B.P. 20, El Jadida, Morocco
2 UFR Mathématiques Appliquées et Industrielles Faculté des Sciences B.P. 20, El Jadida, Marocco 
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     title = {Existence result for nonlinear parabolic problems with $L^1$-data},
     journal = {Applicationes Mathematicae},
     pages = {483--508},
     year = {2010},
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     doi = {10.4064/am37-4-6},
     language = {en},
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Abderrahmane El Hachimi; Jaouad Igbida; Ahmed Jamea. Existence result for nonlinear parabolic problems with $L^1$-data. Applicationes Mathematicae, Tome 37 (2010) no. 4, pp. 483-508. doi: 10.4064/am37-4-6

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