Geodesic
Reduced Measures Associated with Parabolic Problems
Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 10-31

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We study the existence and the properties of reduced measures for the parabolic equations $\partial_tu-\Delta u+g(u)=0$ in $\Omega\times(0,\infty)$ subject to the conditions (P): $u=0$ on $\partial\Omega\times(0,\infty)$, $u(x,0)=\mu$ and (P$'$): $u=\mu'$ on $\partial\Omega\times(0,\infty)$, $u(x,0)=0$, where $\mu$ and $\mu'$ are positive Radon measures and $g$ is a continuous nondecreasing function. 
@article{TRSPY_2008_260_a1,
     author = {W. Al Sayed and M. Jazar and L. V\'eron},
     title = {Reduced {Measures} {Associated} with {Parabolic} {Problems}},
     journal = {Informatics and Automation},
     pages = {10--31},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a1/}
}
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W. Al Sayed; M. Jazar; L. Véron. Reduced Measures Associated with Parabolic Problems. Informatics and Automation, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 10-31. http://geodesic.mathdoc.fr/item/TRSPY_2008_260_a1/