arXiv subjects

Wenhui Chen

Publications and source records attributed to Wenhui Chen.

At least 55 records · Page 3Linked to original sources

arXiv2024

Large time behavior for the hyperbolic-parabolic coupled system with the regularity-loss structure

This paper considers the hyperbolic-parabolic coupled system, arising from the generalized thermoelastic coupled system, in the whole space $\mathbb{R}^n$. We study some qualitative properties for an energy term by diagonalization procedures, and for the solution by the WKB analysis. Particularly, we derive new large time asymptotic profiles with the regularity-loss structure (from the biharmonic parabolic equation and the diffusion wave equation with the Riesz potential operator) and optimal decay estimates with suitable higher regularities for the Cauchy data. Finally, we discover that the wave equation with the Riesz potential dissipation is a large time approximated model of our hyperbolic-parabolic coupled system.

math.AP↗

arXiv2024

Some asymptotic profiles for the viscous Moore-Gibson-Thompson equation in the $L^q$ framework

This manuscript studies some qualitative properties of solutions to the Cauchy problem for the viscous Moore-Gibson-Thompson (MGT) equation. For one thing, by applying the WKB analysis and diagonalization procedure, we derive some $L^p-L^q$ decay estimates and the large time asymptotic profile for a suitable energy term, which provides a new way to treat higher order MGT-type coupled systems. For another, we obtain the global (in time) singular limits in the $L^q$ framework and the higher order asymptotic profile with respect to small thermal relaxation via the multi-scale analysis and the Fourier analysis. Especially, provided the incompatible initial condition between the viscous MGT equation and the strongly damped wave equation, the formation of initial layer is rigorously justified.

math.AP↗

arXiv2024

Enhancing Human Experience in Human-Agent Collaboration: A Human-Centered Modeling Approach Based on Positive Human Gain

Existing game AI research mainly focuses on enhancing agents' abilities to win games, but this does not inherently make humans have a better experience when collaborating with these agents. For example, agents may dominate the collaboration and exhibit unintended or detrimental behaviors, leading to poor experiences for their human partners. In other words, most game AI agents are modeled in a "self-centered" manner. In this paper, we propose a "human-centered" modeling scheme for collaborative agents that aims to enhance the experience of humans. Specifically, we model the experience of humans as the goals they expect to achieve during the task. We expect that agents should learn to enhance the extent to which humans achieve these goals while maintaining agents' original abilities (e.g., winning games). To achieve this, we propose the Reinforcement Learning from Human Gain (RLHG) approach. The RLHG approach introduces a "baseline", which corresponds to the extent to which humans primitively achieve their goals, and encourages agents to learn behaviors that can effectively enhance humans in achieving their goals better. We evaluate the RLHG agent in the popular Multi-player Online Battle Arena (MOBA) game, Honor of Kings, by conducting real-world human-agent tests. Both objective performance and subjective preference results show that the RLHG agent provides participants better gaming experience.

cs.HC↗

arXiv2024

On the Cauchy problem for acoustic waves in hereditary fluids: decay properties and inviscid limits

This manuscript considers the viscous/inviscid Moore-Gibson-Thompson (MGT) equations with memory of type I in the whole space $\mathbb{R}^n$. For one thing, associating with a new condition on initial data, we derive the optimal $L^2$ estimates and the optimal leading term of the acoustic velocity potential for large time, in which we analyze different contributions from viscous, thermally relaxing, as well as hereditary fluids on large time asymptotic behavior for the acoustic waves models. For another, via the multi-scale analysis and energy methods in the Fourier space, we demonstrate the $L^{\infty}$ inviscid limits in the sense of the diffusivity of sound tending to zero, which match our WKB expansion of the solution. Finally, we give a further application of our results on large time behavior for the nonlinear Jordan-MGT equation in viscous hereditary fluids.

math.AP↗

arXiv2023

Large time behavior for the nonlinear dissipative Boussinesq equation

In this paper, we study the nonlinear dissipative Boussinesq equation in the whole space $\mathbb{R}^n$ with $L^1$ integrable data. As our preparations, the optimal estimates as well as the optimal leading terms for the linearized model are derived by performing the WKB analysis and the Fourier analysis. Then, under some conditions on the power $p$ of nonlinearity, we demonstrate global (in time) existence of small data Sobolev solutions with different regularities to the nonlinear model by applying some fractional order interpolations, where the optimal growth ($n=2$) and decay ($n\geqslant 3$) estimates of solutions for large time are given. Simultaneously, we get a new large time asymptotic profile of global (in time) solutions. These results imply some influence of dispersion and dissipation on qualitative properties of solution.

math.AP↗

arXiv2023

Asymptotic behavior of solutions for the thermoviscous acoustic systems

We study some asymptotic properties of solutions for the acoustic coupled systems in thermoviscous fluids which was proposed by [Karlsen-Bruus, \emph{Phys. Rev. E} (2015)]. Basing on the WKB analysis and the Fourier analysis, we derive optimal estimates and large time asymptotic profiles of the energy term via diagonalization procedure, and of the velocity potential via reduction methodology. We found that the wave effect has a dominant influence for lower dimensions comparing with thermal-viscous effects. Moreover, by employing suitable energy methods, we rigorously demonstrate global (in time) inviscid limits as the momentum diffusion coefficient vanishes, whose limit model can be regarded as the thermoelastic acoustic systems in isotropic solids. These results explain some influence of the momentum diffusion on asymptotic behavior of solutions.

math.AP↗

arXiv2023

The influence of viscous dissipations on the nonlinear acoustic wave equation with second sound

We study the effect of a viscous dissipation on the Cauchy problem for a Cattaneo-type model in nonlinear acoustics, established by applying the Lighthill approximation for the viscous or inviscid fluid model. The contribution of this paper is twofold. For the nonlinear viscous Cattaneo-type model involving a fractional Laplacian $(-Δ)^α$ in the viscous damping with $α\in[0,1]$, we derive optimal decay rates for global (in time) solutions with small data in certain Sobolev spaces. Furthermore, by introducing a threshold $α=1/2$ for the power of the fractional viscous dissipation, we derive an anomalous diffusion profile when $α\in[0,1/2)$ and a diffusion wave profile when $α\in[1/2,1]$ for large-time. Whereas, for the nonlinear inviscid Cattaneo-type model (or the Jordan-Moore-Gibson-Thompson equation in the critical case), we obtain the blow-up of the energy solutions in finite time under suitable assumptions for the initial data. Thus, the presence of a viscous dissipation in the nonlinear Cattaneo-type model is a criterion for the global (in time) existence and blow-up of solutions.

math.AP↗

arXiv2023

On the critical regularity of nonlinearities for semilinear classical wave equations

In this paper, we consider the Cauchy problem for semilinear classical wave equations \begin{equation*} u_{tt}-Δu=|u|^{p_S(n)}μ(|u|) \end{equation*} with the Strauss exponent $p_S(n)$ and a modulus of continuity $μ=μ(τ)$, which provides an additional regularity of nonlinearities in $u=0$ comparing with the power nonlinearity $|u|^{p_S(n)}$. We obtain a sharp condition on $μ$ as a threshold between global (in time) existence of small data radial solutions by deriving polynomial-logarithmic type weighted $L^{\infty}_tL^{\infty}_r$ estimates, and blow-up of solutions in finite time even for small data by applying iteration methods with slicing procedure. These results imply the critical regularity of source nonlinearities for semilinear classical wave equations.

math.AP↗

arXiv2023

BARS: A Benchmark for Airport Runway Segmentation

Airport runway segmentation can effectively reduce the accident rate during the landing phase, which has the largest risk of flight accidents. With the rapid development of deep learning (DL), related methods achieve good performance on segmentation tasks and can be well adapted to complex scenes. However, the lack of large-scale, publicly available datasets in this field makes the development of methods based on DL difficult. Therefore, we propose a benchmark for airport runway segmentation, named BARS. Additionally, a semiautomatic annotation pipeline is designed to reduce the annotation workload. BARS has the largest dataset with the richest categories and the only instance annotation in the field. The dataset, which was collected using the X-Plane simulation platform, contains 10,256 images and 30,201 instances with three categories. We evaluate eleven representative instance segmentation methods on BARS and analyze their performance. Based on the characteristic of an airport runway with a regular shape, we propose a plug-and-play smoothing postprocessing module (SPM) and a contour point constraint loss (CPCL) function to smooth segmentation results for mask-based and contour-based methods, respectively. Furthermore, a novel evaluation metric named average smoothness (AS) is developed to measure smoothness. The experiments show that existing instance segmentation methods can achieve prediction results with good performance on BARS. SPM and CPCL can effectively enhance the AS metric while modestly improving accuracy. Our work will be available at https://github.com/c-wenhui/BARS.

cs.CV↗

arXiv2023

Critical exponent and sharp lifespan estimates for semilinear third-order evolution equations

We study semilinear third-order (in time) evolution equations with fractional Laplacian $(-Δ)^σ$ and power nonlinearity $|u|^p$, which was proposed by Bezerra-Carvalho-Santos [2] recently. In this manuscript, we obtain a new critical exponent $p=p_{\mathrm{crit}}(n,σ):=1+\frac{6σ}{\max\{3n-4σ,0\}}$ for $n\leqslant\frac{10}{3}σ$. Precisely, the global (in time) existence of small data Sobolev solutions is proved for the supercritical case $p>p_{\mathrm{crit}}(n,σ)$, and weak solutions blow up in finite time even for small data if $1<p\leqslant p_{\mathrm{crit}}(n,σ)$. Furthermore, to more accurately describe the blow-up time, we derive new and sharp upper bound as well as lower bound estimates for the lifespan in the subcritical case and the critical case.

math.AP↗

arXiv2022

Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations

In this paper, we consider the linearized compressible Navier-Stokes equations in the whole space $\mathbb{R}^n$. Concerning initial datum with suitable regularities, we introduce a new threshold $|\mathbb{B}_0|=0$ to distinguish different large-time behaviors. Particularly in the lower-dimensions, optimal growth estimates ($n=1$ polynomial growth, $n=2$ logarithmic growth) hold when $|\mathbb{B}_0|>0$, whereas optimal decay estimates hold when $|\mathbb{B}_0|=0$. Furthermore, we derive asymptotic profiles of solutions with weighted $L^1$ datum as large-time.

math.AP↗

arXiv2022

Optimal large-time estimates and singular limits for thermoelastic plate equations with the Fourier law

In this paper, we study asymptotic behaviors for classical thermoelastic plate equations with the Fourier law of heat conduction in the whole space $\mathbb{R}^n$, where we introduce a reduction methodology basing on third-order (in time) differential equations and refined Fourier analysis. We derive optimal growth estimates when $n\leqslant 3$, bounded estimates when $n=4$, and decay estimates when $n\geqslant 5$ for the vertical displacement in the $L^2$ norm. Particularly, the new critical dimension $n=4$ for distinguishing the decisive role between the plate model and the Fourier law of heat conduction is discovered. Moreover, concerning the small thermal parameter in the temperature equation, we study the singular limit problem. We not only show global (in time) convergence of the vertical displacements between thermoelastic plates and structurally damped plates, but also rigorously demonstrate a new second-order profile of the solution. Our methodology can settle several closely related problems in thermoelasticity.

math.AP↗

arXiv2022

A note on asymptotic profiles for the thermoelastic plate system

We investigate the Cauchy problem for the thermoelastic plate system associated with Newton's law of cooling, where optimal growth ($n\leqslant 4$) or decay ($n\geqslant 5$) estimates and asymptotic profiles of solutions for large-time are studied. Especially, the additional lower-order term in the temperature equation weakens decay rates of the vertical displacement, and leads to a new leading term comparing with the classical thermoelastic plates.

math.AP↗

arXiv2022

Large-time asymptotic behaviors for the classical thermoelastic system

In this paper, we study the classical thermoelastic system with Fourier's law of heat conduction in the whole space $\mathbb{R}^n$ when $n=1,2,3$, particularly, asymptotic profiles for its elastic displacement as large-time. We discover optimal growth estimates of the elastic displacement when $n=1,2$, whose growth rates coincide with those for the free wave model, whereas when $n=3$ the optimal decay rate is related to the Gaussian kernel. Furthermore, under a new condition for weighted datum, the large-time optimal leading term is firstly introduced by the combination of diffusion-waves, the heat kernel and singular components. We also illustrate a second-order profile of solution by diffusion-waves with weighted $L^1$ datum as a by-product. These results imply that wave-structure large-time behaviors hold only for the one- and two-dimensional thermoelastic systems.

math.AP↗

arXiv2022

Large-time asymptotic behaviors for linear Blackstock's model of thermoviscous flow

In the classical theory of acoustic waves, Blackstock's model was proposed in 1963 to characterize the propagation of sound in thermoviscous fluids. In this paper, we investigate large-time asymptotic behaviors of the linear Cauchy problem for general Blackstock's model (that is, without Becker's assumption on monatomic perfect gases). We derive first- and second-order asymptotic profiles of solution as $t\gg1$ by applying refined WKB analysis and Fourier analysis. Our results not only improve optimal estimates in [Chen-Ikehata-Palmieri, \emph{Indiana Univ. Math. J.} (2023)] for lower dimensional cases, but also illustrate the optimal leading term and novel second-order profiles of solution with additional weighted $L^1$ data.

math.AP↗

arXiv2022

Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in the viscous case

In this paper, we study large-time behaviors for a fundamental model in nonlinear acoustics, precisely, the viscous Jordan-Moore-Gibson-Thompson (JMGT) equation in the whole space $\mathbb{R}^n$. This model describes nonlinear acoustics in perfect gases under irrotational flow and equipping Cattaneo's law of heat conduction. By employing refined WKB analysis and Fourier analysis, we derive first- and second-order asymptotic profiles of solution to the Moore-Gibson-Thompson (MGT) equation as $t\gg 1$, which illustrates novel optimal estimates for the solutions even subtracting its profiles. Concerning the nonlinear JMGT equation, via suggesting a new decomposition of nonlinear portion, we investigate the existence and large-time profiles of global (in time) small data Sobolev solutions with suitable regularity. These results help bridge a new connection between the JMGT equation and diffusion-waves as $t\gg1$.

math.AP↗

arXiv2022

A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term

In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in $\mathbb{R}^n$, which can be represented by the Riemann-Liouville fractional integral of order $1-γ$ with $γ\in(0,1)$. Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of $γ$, on the blow-up range between the effective case and the non-effective case.

math.AP↗

arXiv2021

Decay properties and asymptotic behaviors for a wave equation with general strong damping

In this paper, we study the Cauchy problem for a wave equation with general strong damping $-μ(|D|)Δu_t$ motivated by [Tao, Anal. PDE (2009)] and [Ebert-Girardi-Reissig, Math. Ann. (2020)]. By employing energy methods in the Fourier space and WKB analysis, we derive decay estimates for solutions under a large class of $μ(|D|)$. In particularly, a threshold $\lim\nolimits_{|ξ|\to\infty}μ(|ξ|)=\infty$ is discovered for the regularity-loss phenomenon, where $μ(|ξ|)$ denotes the symbol of $μ(|D|)$. Furthermore, we investigate different asymptotic profiles of solution with additionally $L^1$ initial data, where some refined estimates in the sense of enhanced decay rate and reduced regularity are found. The derived results almost cover the known results with sufficiently small loss.

math.AP↗