arXiv subjects

Ruijing Wang

Publications and source records attributed to Ruijing Wang.

4 recordsLinked to original sources

arXiv2026

Global Existence for Reaction-diffusion Equations with State-Dependent Delay and Fast-growing Nonlinearities

This work aims to study the initial-boundary value problem of the reaction-diffusion equation with state-dependent delay $\pa_{t}u-\Delta u=f(u)+g(u,u(t-\tau(t,u_t)))+h(t,x)$ in a bounded domain. We establish the global existence of the problem under suitable dissipative-type structural conditions, allowing both nonlinear terms $f$ and $g$ to have arbitrary polynomial growth rates. Another highlight in this work is that, we significantly relax the continuity assumptions imposed on the delay functions.

math.AP↗

arXiv2024

Global Existence, Regularity, and Dissipativity of Reaction-diffusion Equations with State-dependent Delay and Supercritical Nonlinearities

This work aims to study the initial-boundary value problem of the reaction-diffusion equation $\pa_{t}u-\Delta u=f(u)+g(u(t-\tau(t,u_t)))+h(t,x)$ in a bounded domain with state-dependent delay and supercritical nonlinearities. We establish the global existence and discuss the regularity and dissipativity of the problem under weaker assumptions. In particular, the existence of a global pullback attractor is proved regardless of uniqueness.

math.AP↗

arXiv2022

A Note on the Krein-Rutman Theorem for Sectorial Operators

In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that they contain some information on the generalized eigenspaces associated with non-principal eigenvalues, which are helpful in the study of the dynamics of evolution equations in ordered Banach spaces.

math.FA↗

arXiv2020

New Schemes for Solving the Principal Eigenvalue Problems of Perron-like Matrices via Polynomial Approximations of Matrix Exponentials

A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,μ<s$ for any other eigenvalue $μ$. Nonnegative matrices and symmetric ones are typical examples of this class of matrices. The main purpose of this paper is to develop a set of new schemes to compute the principal eigenvalues of Perron-like matrices and the associated generalized eigenspaces by using polynomial approximations of matrix exponentials. Numerical examples show that these schemes are effective in practice.

math.NA↗