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MSC: 35K35, 35K59, 47H05
Porous media equations, fast diffusion equations, subdifferential operators
This paper considers the initial-boundary value problem for the nonlinear diffusion equation with the perturbation term $$ u_t + (-\Delta+1)\beta(u) + G(u) = g \quad \mbox{in}\ \Omega\times(0, T) $$ in an unbounded domain $\Omega \subset \mathbb{R}^N$ with smooth bounded boundary, where $N \in \mathbb{N}$, $T>0$, $\beta$, is a single-valued maximal monotone function on $\mathbb{R}$, e.g., $$ \beta(r) = |r|^{q-1}r\ (q > 0, q\neq1) $$ and $G$ is a function on $\mathbb{R}$ which can be regarded as a Lipschitz continuous operator from $(H^1(\Omega))^{*}$ to $(H^1(\Omega))^{*}$. The present work establishes existence and estimates for the above problem.
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