| Abstract: |
| This talk deals with the moisture transport model for porous materials,
$$
\dfrac{\partial}{\partial t}\psi(u) = \nabla\cdot\big(\lambda(u)\nabla(u+g)\big), \quad t \in (0,T),\ x \in \Omega
$$
under the Neumann boundary condition $\frac{\partial}{\partial n}(u+g)=0$ for $t \in (0,T)$ and $x \in \partial \Omega$ and the initial condition, where $T>0$, $\Omega\subset\mathbb R^N$ ($N\in\mathbb N$) is a bounded domain with smooth boundary, $\psi, \lambda, g$ are given functions satisfying some conditions. In the previous work, global weak solvability and uniqueness were shown under the restriction that $\frac{\lambda}{\psi`}$ is constant in the one-dimensional setting. The purpose of this talk is to relax these restrictions and to give an elementary proof of global weak solvability of the above $N$-dimensional initial-boundary value problem by using the theory for linear operators. |
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