A5039309752- Stability and Controllability of Differential Equations
- Advanced Mathematical Modeling in Engineering
- Numerical methods in inverse problems
- Stochastic processes and financial applications
- Nonlinear Differential Equations Analysis
- Liver physiology and pathology
- Extracellular vesicles in disease
- Nonlinear Partial Differential Equations
- Contact Mechanics and Variational Inequalities
- Phagocytosis and Immune Regulation
Central South University
2024
Mayo Clinic in Florida
2024
Liver fibrosis is characterized by the activation of perivascular hepatic stellate cells (HSCs), release fibrogenic nanosized extracellular vesicles (EVs), and increased HSC glycolysis. Nevertheless, how glycolysis in HSCs coordinates amplification through tissue zone-specific pathways remains elusive. Here, we demonstrate that HSC-specific genetic inhibition reduced liver fibrosis. Moreover, spatial transcriptomics revealed a fibrosis-mediated up-regulation EV-related pericentral zone,...
This paper is concerned with impulse approximate controllability for stochastic evolution equations controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The problem seeks to identify an characterized by the minimum among all feasible controls, guiding system's solutions from initial state within a fixed interval toward predetermined target while find (among certain constraint set), which steers solution of equation given set as soon...
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on whole Euclidean space is established. This paper generalizes earlier results in [29] and [17] from domain to an unbounded one. The proof based locally parabolic-type frequency function method. An observability measurable sets time same also derived.
This paper endeavours to directly establish the observability inequality of backward stochastic heat equations involving a Lévy process for measurable sets. As an immediate application, we attain approximate controllability forward featuring process. Subsequently, embark upon formulation nuanced optimization problem, encompassing both determination optimal actuator location and its associated minimum norm control. is elegantly cast as two-person zero-sum game problem. We then proceed...
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on whole Euclidean space is established. This paper generalizes earlier results in [29] and [17] from domain to an unbounded one. The proof based locally parabolic-type frequency function method. An observability measurable sets time same also derived.
In this study, we employ the established Carleman estimates and propagation of smallness from measurable sets for real analytic functions, along with telescoping series method, to establish an observability inequality degenerate parabolic equation over subsets in time-space domain. As a direct application, formulate captivating Stackelberg-Nash game problem provide proof existence its equilibrium. Additionally, characterize set equilibria delve into analysis norm optimal control problem.
This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of control, followed discussion its properties. then explore equivalence between subsequently establish bang-bang property control. These problems, to best our knowledge, are among first discuss in case.
This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in context of approximate controllability degenerate parabolic equations. We propose a formulation optimization problem that encompasses both and its associated control. Specifically, we transform into two-person zero-sum game problem, resulting development four equivalent formulations. Finally, establish crucial result solution to relaxed serves as an classical problem.
The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination spectral inequalities, interpolation and telegraph series method as our primary tools directly establish inequalities. Furthermore, we explore three specific equations application examples: degenerate equation, fourth order parabolic equation heat equation. It is noteworthy that these can be rendered null controllability with only one...