arXiv subjects

Yansheng Ma

Publications and source records attributed to Yansheng Ma.

3 recordsLinked to original sources

arXiv2026

Null controllability of one-dimensional quasilinear parabolic equations via multiplicative controls

This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control forcing the solution rest at a time $T>0$, we need to establish the decay property of solutions for the system without control first. We have obtained decay estimates for the $L^\infty$-norm and the $H^1$-norm of solutions to the homogenous quasilinear parabolic equations. Notably, the decay of the $L^\infty$-norm requires no smallness condition on the initial data, whereas the decay of the $H^1$-norm requires that the $L^\infty$-norm remains small. Based on the decay estimates and maximum modulus estimate of solutions to quasilinear parabolic equations, together with the local null controllability of quasilinear parabolic equations under additive controls, we prove the null controllability of the quasilinear parabolic equations via multiplicative controls. As a byproduct, we also obtain the global null controllability for large time to the quasilinear parabolic equations via additive controls. Given that the controllability under multiplicative control is achieved over a long time horizon, we finally investigate the existence of time optimal control.

math.OC↗

arXiv2025

Global classical solutions to a two-dimensional chemotaxis-fluid system involving signal-dependent degenerate diffusion

This paper is concerned with the two-dimensional chemotaxis-fluid model \begin{equation*} \begin{cases} n_t+u\cdot\nabla n=Δ(nϕ(v))+μn(1-n),\\ v_t+u\cdot\nabla v=Δv-nv,\\ u_t+ κ(u\cdot\nabla) u=Δu+n\nablaΦ-\nabla P, \quad\nabla\cdot u=0, \end{cases} \end{equation*} accounting for signal-dependent motilities of microbial populations interacting with an incompressible liquid through transport and buoyancy, where the suitably smooth function $ϕ$ satisfies $ϕ>0$ on $(0,\infty)$ with $ϕ(0)=0$ and $ϕ'(0)>0$, and the parameter $μ\geq 0$. For all reasonably regular initial data, if $μ=0$, the corresponding initial boundary value problem possesses global classical solutions with a smallness condition on $\int_Ωn_0$; whereas if $μ>0$, this problem possesses global bounded classical solutions, which can converge toward (1,0,0) as time tends to infinity when a certain small mass is imposed on the initial data $v_0$. These results extend recent results for the fluid-free system to one in a Navier-Stokes fluid environment.

math.AP↗

arXiv2022

Global solutions to the Nernst-Planck-Euler system on bounded domain

We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two species or the diffusivities and the absolute values of ionic valences are the same if the species are arbitrarily many. In particular, the boundary conditions for the ions are allowed to be inhomogeneous. The proof is based on the energy estimates, integration along the characteristic line and the regularity theory of elliptic and parabolic equations.

math.AP↗