46 citations · 79 across the 28 of their papers we have counts for
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Proof of Proposition 3.1 in the paper titled "Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions''
Qiaoling Chen, Jun Zheng, Guchuan Zhu
We provide a detailed proof of Proposition 3.1 in the paper titled ``Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions…
Approximations of Lyapunov functions for ISS analysis of a class of nonlinear parabolic PDEs
Jun Zheng, Guchuan Zhu
This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equa…
A Note on the Maximum Principle-based Approach for ISS Analysis of Higher Dimensional Parabolic PDEs with Variable Coefficients
Jun Zheng, Guchuan Zhu
This paper presents a maximum principle-based approach in the establishment of input-to-state stability (ISS) for a class of nonlinear parabolic partial differential equations (PDE…
A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances
Jun Zheng, Guchuan Zhu
In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with boun…
A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances
Jun Zheng, Guchuan Zhu
This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers' equation. The developed approach is a combin…
ISS with Respect to Boundary and In-domain Disturbances for a Coupled Beam-String System
Jun Zheng, Hugo Lhachemi, Guchuan Zhu +1
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of b…
Regularity in the two-phase free boundary problems under non-standard growth conditions
Jun Zheng
In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_γ(u)=\int_Ω\big(f(x,\nabla u)+λ_{+} (u^{+})^γ+λ_{-}(u^{-})^…
A minimum problem with free boundary and subcritical growth in Orlicz spaces
Jun Zheng, Leandro S. Tavares, Claudianor O. Alves
The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_Ω(G(|\nabla u|)+qF(u^+)+hu+λ_{+}χ_{\{u>0\}} )\text{d}x\rightarrow\text{…
The obstacle problem for nonlinear degenerate equations with -data
Jun Zheng, Binhua Feng, Zhihua Zhang
The aim of this paper is to study the obstacle problem with an elliptic operator having degenerate coercivity. We prove the existence of an entropy solution to the obstacle problem…