108 research outputs found
Global existence of weak solution to the heat and moisture transport system in fibrous porous media
This paper is concerned with theoretical analysis of a heat and moisture
transfer model arising from textile industries, which is described by a
degenerate and strongly coupled parabolic system. We prove the global (in time)
existence of weak solution by constructing an approximate solution with some
standard smoothing. The proof is based on the physcial nature of gas
convection, in which the heat (energy) flux in convection is determined by the
mass (vapor) flux in convection.Comment: 19 page
Numerical analysis of nonlinear subdiffusion equations
We present a general framework for the rigorous numerical analysis of
time-fractional nonlinear parabolic partial differential equations, with a
fractional derivative of order in time. The framework relies
on three technical tools: a fractional version of the discrete Gr\"onwall-type
inequality, discrete maximal regularity, and regularity theory of nonlinear
equations. We establish a general criterion for showing the fractional discrete
Gr\"onwall inequality, and verify it for the L1 scheme and convolution
quadrature generated by BDFs. Further, we provide a complete solution theory,
e.g., existence, uniqueness and regularity, for a time-fractional diffusion
equation with a Lipschitz nonlinear source term. Together with the known
results of discrete maximal regularity, we derive pointwise norm
error estimates for semidiscrete Galerkin finite element solutions and fully
discrete solutions, which are of order (up to a logarithmic factor)
and , respectively, without any extra regularity assumption on
the solution or compatibility condition on the problem data. The sharpness of
the convergence rates is supported by the numerical experiments
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