293 citations · 1.1k across the 28 of their papers we have counts for
28 papers
Simultaneous recovery of multiple parameters in nonlocal diffusion equations from internal measurements
Kai Yu, Zhiyuan Li, Yikan Liu
This paper is devoted to simultaneously recovering multiple parameters from internal measurements for nonlocal diffusion equations. The uniqueness of the inverse problem is establi…
Threshold dynamics in time-delay systems: polynomial -control in a pressing process and connections to blow-up
Masato Kimura, Hirotaka Kuma, Yikan Liu +3
This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized -control meth…
Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
Kai Yu, Zhiyuan Li, Yikan Liu
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the…
Sharp decay estimates and numerical analysis for weakly coupled systems of two subdiffusion equations
Zhiyuan Li, Yikan Liu, Kazuma Wada
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coeff…
Energy decay of nonlocal viscoelastic equations with nonlinear damping and polynomial nonlinearity
Qingqing Peng, Yikan Liu
This paper is concerned with the energy decay of a viscoelastic variable coefficient wave equation with nonlocality in time as well as nonlinear damping and polynomial nonlinear te…
Exponential stability for an infinite memory wave equation with frictional damping and logarithmic nonlinear terms
Qingqing Peng, Yikan Liu
This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a…
Blow-up for time-fractional diffusion equations with superlinear convex semilinear terms
Xinchi Huang, Yikan Liu, Masahiro Yamamoto
This article is concerned with a semilinear time-fractional diffusion equation with a superlinear convex semilinear term in a bounded domain with the homogeneous Dirichlet, Neu…
Recovery of Multiple Parameters in Subdiffusion from One Lateral Boundary Measurement
Siyu Cen, Bangti Jin, Yikan Liu +1
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while…
Blowup in -norm and global existence for time-fractional diffusion equations with polynomial semilinear terms
Giuseppe Floridia, Yikan Liu, Masahiro Yamamoto
This article is concerned with semilinear time-fractional diffusion equations with polynomial nonlinearity in a bounded domain with the homogeneous Neumann boundary condi…
Uniqueness of inverse source problems for time-fractional diffusion equations with singular functions in time
Yikan Liu, Masahiro Yamamoto
We consider a fractional diffusion equations of order whose source term is singular in time: , , where belong…
Initial-boundary value problems for coupled systems of time-fractional diffusion equations
Zhiyuan Li, Xinchi Huang, Yikan Liu
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamen…
Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior
Yikan Liu, Masahiro Yamamoto
As the most significant difference from parabolic equations, long-time or short-time behavior of solutions to time-fractional evolution equations is dominated by the fractional ord…
Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions
Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
In this paper, we obtain the sharp uniqueness for an inverse -source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum pos…
Uniqueness of Inverse Source Problems for General Evolution Equations
Yavar Kian, Yikan Liu, Masahiro Yamamoto
In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interio…
Inverse moving source problem for time-fractional evolution equations: Determination of profiles
Yikan Liu, Guanghui Hu, Masahiro Yamamoto
This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order in time. In the first…
Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement
Yavar Kian, Zhiyuan Li, Yikan Liu +1
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded…
Inverse moving source problem for fractional diffusion(-wave) equations: Determination of orbits
Guanghui Hu, Yikan Liu, Masahiro Yamamoto
This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R…
Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations
Zhiyuan Li, Yikan Liu, Masahiro Yamamoto
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractio…
Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
Yikan Liu, Zhiyuan Li, Masahiro Yamamoto
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order . Our surve…
Unique continuation property with partial information for two-dimensional anisotropic elasticity systems
Jin Cheng, Yikan Liu, Yanbo Wang +1
In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous el…
Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction
Jie Yu, Yikan Liu, Masahiro Yamamoto
In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numeric…
Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations
Daijun Jiang, Zhiyuan Li, Yikan Liu +1
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the…
Strong Maximum Principle for Multi-Term Time-Fractional Diffusion Equations and its Application to an Inverse Source Problem
Yikan Liu
In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of pra…
Theoretical stability and numerical reconstruction for an inverse source problem for hyperbolic equations
Daijun Jiang, Yikan Liu, Masahiro Yamamoto
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a ne…