Reduced measures associated to parabolic problems

Sayed, Waad Al; Jazar, Mustapha; Veron, Laurent

Reduced measures associated to parabolic problems

Authors

Sayed, Waad Al

Jazar, Mustapha

Veron, Laurent

Description

We study the existence and the properties of the reduced measures for the parabolic equations $\partial_tu-Δu+g(u)=0$ in $Ω\times (0,\infty)$ subject to the conditions ($P$): $u=0$ on $\partialΩ\times (0,\infty)$, $u(x,0)=μ$ and ($P'$): $u=μ'$ on $\partialΩ\times (0,\infty)$, $u(x,0)=0$ where $μ$ and $μ'$ are positive Radon measures and $g$ a continuous nondecreasing function