A5103109265- Advanced Mathematical Modeling in Engineering
- Numerical methods in inverse problems
- Stability and Controllability of Differential Equations
- Nonlinear Partial Differential Equations
- Differential Equations and Numerical Methods
- Fractional Differential Equations Solutions
- Numerical methods in engineering
- Thermoelastic and Magnetoelastic Phenomena
- Advanced Mathematical Physics Problems
- Mathematical and Theoretical Epidemiology and Ecology Models
- Stochastic processes and financial applications
- advanced mathematical theories
- Blind Source Separation Techniques
- Soil, Finite Element Methods
- Nonlinear Waves and Solitons
- Chemical Reactions and Mechanisms
- Ultrasonics and Acoustic Wave Propagation
- Advanced Battery Materials and Technologies
- Energy Load and Power Forecasting
- Nonlinear Differential Equations Analysis
- Advanced Adaptive Filtering Techniques
- Structural Load-Bearing Analysis
- Hydraulic and Pneumatic Systems
- Microwave Imaging and Scattering Analysis
- Welding Techniques and Residual Stresses
Nanjing University of Information Science and Technology
2014-2024
China Southern Power Grid (China)
2024
Commercial Aircraft Corporation of China (China)
2012
Southeast University
2009-2012
Shanghai Jiao Tong University
2002
In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is the backward equation with singular weight function. Combining estimate and an approximate argument, prove null controllability of forward gradient term. second regular weighted function, based on which obtain Lipschitz stability inverse problem determining random source depending only time in
Abstract In this note we illuminate that the small condition on initial data u 0 in Theorem 4.1 of Yin and Jin ( Math. Meth. Appl. Sci. 2007; 30 (10):1147–1167) can be removed for case p −1< q <1. Precise decay estimates solution are also obtained. Copyright © 2007 John Wiley & Sons, Ltd.
We study an inverse problem of determining a spatially varying source term in thermoelastic medium with memory effect. The coupling phenomena between elasticity and heat as well the effect make such very complicated. firstly prove pointwise Carleman estimate for general strongly coupled hyperbolic system, then obtain system. Based on this estimate, we finally establish Hölder stability only by making displacement measurement given subdomain sufficiently large times, provided be known near...
We study the inverse problem of determining two spatially varying coefficients in a thermoelastic model with following observation data: displacement subdomain ω satisfying ∂ω⊃∂Ω along sufficiently large time interval, both and temperature at suitable over whole spatial domain. Based on Carleman estimate hyperbolic–parabolic system, we prove Lipschitz stability uniqueness for this under some priori information.
This paper concerns an inverse problem for integro-differential equation related to the Basset problem. The aims determine a weakly singular term from time trace at fixed point . We use maximum principle operator derive uniqueness of Additionally, we prove existence and direct with general kernel function. MSC: 35L05, 35L10, 35R09, 35R30.
In this paper, we establish a Carleman estimate for strongly damped wave equation in order to solve coefficient inverse problems of retrieving stationary potential from single time‐dependent Neumann boundary measurement on suitable part the boundary. This problem is equation. We prove uniqueness and local stability results problem. The proof relies certain energy estimates hyperbolic with term. Moreover, method could be used similar an integro‐differential memory kernel. Copyright © 2012...
The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem porous medium equation , is studied. Sufficient conditions about and decay estimates are obtained by using -integral model estimate methods two crucial lemmas on differential inequality.
This article concerns an inverse problem for a strongly coupled reaction-diffusion system, which has many applications including the cross diffusion resulted from influence of one component on another. aims to determine spatially varying coefficient in system internal observation data arbitrary subdomain. We use new Carleman estimate derive Hölder stability this problem. Different existing methods dealing with weakly or such as Fan & Chen (2012, Stability estimates parabolic system. Tamkang...
Abstract This paper is concerned with the inverse problem for determining space-dependent source and initial value simultaneously in a parabolic equation from two over-specified measurements. By means of transforming information into term obtaining combined term, converted homogeneous conditions. Then considered formulated regularized minimization problem, which implemented by finite element method based on solving sequence well-posed direct problems. The uniqueness solutions are proved...
This paper concerns a backward problem for linear stochastic Kuramoto–Sivashinsky equation, which aims to reconstruct the initial value from mean measurement at terminal time. By transforming into regularized optimization one, regularization method together with its numerical implementation in finite dimensional space is proposed solving problem. Finally, we show effectiveness of reconstruction by several examples.
Abstract This paper concerns unique continuation for a reaction-diffusion system with cross diffusion, which is drug war describing simple dynamic model of epidemic in an idealized community. We first establish Carleman estimate this strongly coupled system. Then we apply the to prove continuation, means that Cauchy data on any lateral boundary determine solution uniquely whole domain.
In this paper, we consider a null controllability and an inverse source problem for stochastic Grushin equation with boundary degeneracy singularity. We construct two special weight functions to establish Carleman estimates the whole operator singular potential by weighted identity method. One is backward function. then apply it prove any T γ > 0, when our control domain touches line { x = 0}. order study of determining kinds sources simultaneously, other estimate, which forward regular...
We consider the transient drift-diffusion model with fast diffusion terms. This problem is not only degenerate but also singular. first present existence result for general nonlinear diffusivities Dirichlet-Neumann mixed boundary value problem. Then, extinction phenomenon of weak solutions homogeneous Dirichlet studied. Sufficient conditions on and decay estimates are obtained by using -integral estimate method.