arXiv subjects

Jiazhuo Cheng

Publications and source records attributed to Jiazhuo Cheng.

4 recordsLinked to original sources

arXiv2026

Principal spectral theory and variational characterizations for nonlocal coupled cooperative systems and applications

This paper investigates the principal spectral theory of a nonlocal dispersal operator with coupled diffusion and aims to establish a variational characterization of the spectral bound for the case where the system is not strongly coupled. In this setting, a key difficulty arises since the principal eigenfunction may have components that are identically zero, rendering existing generalized eigenvalue methods inapplicable. To overcome this, we reorder the components of the operator using a permutation matrix, thereby decomposing it into suitable suboperators, and characterize the spectral bound of the original operator in terms of the spectral bounds of these suboperators. Building on this principal spectral theory, we provide a variational characterization of the basic reproduction ratio for nonlocal dispersal systems and analyze the dynamical behavior of a class of multi-genotype stem cell regeneration models with epigenetic transitions, both in the presence and absence of gene mutations, without assuming the existence of a principal eigenvalue. Furthermore, we investigate the threshold dynamics when the system is not strongly coupled.

math.AP↗

arXiv2026

Variational characterizations of weighted eigenvalue and basic reproduction ratio for nonlocal dispersal systems and application

The basic reproduction ratio is a crucial threshold parameter in infectious disease models. In nonlocal dispersal systems, its variational characterization is challenging due to the possible absence of a principal eigenvalue caused by non-compactness. In this paper, we aim to establish such a characterization even when the principal eigenvalue does not exist. To this end, we first study the spectral bound of a class of nonlocal dispersal operators, establishing a Collatz-Wielandt characterization as well as a Rayleigh-Ritz characterization when the operator is self-adjoint. Using this, we characterize the unique parameter value at which the spectral bound equals zero, covering both non-degenerate and partially degenerate cases, and subsequently obtain an explicit expression for the basic reproduction ratio. To demonstrate the utility of our theoretical framework, we apply it to a nonlocal dispersal SIS epidemic model with saturated incidence rate. The analysis shows that, in the degenerate case of the saturation coefficient, the limiting behavior of the basic reproduction ratio as the total population tends to zero is strikingly different from that in local diffusion case.

math.AP↗

arXiv2024

Global existence and nonexistence analyses for a magnetic fractional pseudo-parabolic equation

In this paper, we study the initial-boundary value problem for a pseudo-parabolic equation in magnetic fractional Orlicz-Sobolev spaces. First, by employing the imbedding theorems, the theory of potential wells and the Galerkin method, we prove the existence and uniqueness of global solutions with subcritical initial energy, critical initial energy and supercritical initial energy, respectively. Furthermore, we prove the decay estimate of global solutions with sub-sharp-critical initial energy, sharp-critical initial energy and supercritical initial energy, respectively. Specifically, we need to analyze the properties of $ω$-limits of solutions for supercritical initial energy. Next, we establish the finite time blowup of solutions with sub-sharp-critical initial energy and sharp-critical initial energy, respectively. Finally, we discuss the convergence relationship between the global solutions of the evolution problem and the ground state solutions of the corresponding stationary problem.

math.AP↗

arXiv2022

Global existence and finite time blowup for a mixed pseudo-parabolic $p$-Laplacian type equation

This paper concerns the initial-boundary value problem for a mixed pseudo-parabolic $p$-Laplacian type equation. By constructing a family of potential wells, we first present the explicit expression for the depth of potential well, and then prove the existence, uniqueness and decay estimate of global solutions and the blowup phenomena of solutions with subcritical initial energy. Next, we extend parallelly these results to the critical initial energy. Lastly, the existence, uniqueness and asymptotic behavior of global solutions with supercritical initial energy are proved by further analyzing the properties of $ω$-limits of solutions.

math.AP↗