Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

Asymptotic decay under nonlinear and noncoercive dissipative effects for electrical conduction in biological tissues

We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times to a periodic solution when time-periodic boundary data are assigned. The novelty here is that we allow the nonlinearity to be noncoercive. We consider both the homogenized and the non-homogenized version of the problem.

Concentration and homogenization in electrical conduction in heterogeneous media involving the Laplace-Beltrami operator

We study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the composite. This leads to the appearance of a peculiar displacement current governed by a Laplace-Beltrami pseudo-parabolic equation. This pseudo-parabolic character is present also in the homogenized equation, which is obtained by the unfolding technique.

MEMS电火花模型的分析

Analysis of a Model for Electrical Discharge in MEMS

本文研究了MEMS电火花现象的数学模型，通过非线性椭圆-抛物方程组分析电火花的局部存在性，采用紧致性技术证明了弱解的局部时间存在性。

抛物方程拟线性项的同时稳定确定

Simultaneous stable determination of quasilinear terms for parabolic equations

该研究针对抛物方程两类拟线性项的同时恢复反问题，结合线性化、奇异解构造等方法推导了Lipschitz与Hölder稳定性估计，可为数值重构收敛速率分析提供支撑。

Lp regularity for convolution operator equations in Banach spaces

Here we utilize operator--valued Lq-Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integro-differential equations in Rd. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of elliptic differential equations and Cauchy problem for parabolic equations.

A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the ma…