arXiv subjects

Quanguo Zhang

Publications and source records attributed to Quanguo Zhang.

3 recordsLinked to original sources

arXiv2025

The existence and stability for a class of fuzzy fractional boundary value problems constrained by variational inequalities

In this paper, the existence and stability of a new system consisting of fuzzy fractional differential inclusions (FFDIs) with integral boundary conditions and variational inequalities are considered in Euclidean spaces. This system integrates the features of both FFDIs with integral boundary conditions and fractional differential variational inequalities in a unified framework. The existence of solutions for this system is established under some mild conditions. Moreover, the semicontinuity of the solution map for the perturbed system is investigated with respect to parameter perturbations. Finally, we use two numerical examples to show the validity of the above theoretical findings.

math.OC↗

arXiv2024

Nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms

In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in [M. D'Abbicco, A wave equation with structural damping and nonlinear memory, Nonlinear Differ. Equ. Appl. 21 (2014), 751-773]. Moreover, comparing with the existing results, our results do not require any positivity condition of the initial values. The proof of our results is based on the asymptotic properties of solutions for an integral inequality.

math.AP↗

arXiv2022

On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain

In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of Caputo type. Moreover, we also give a result for nonexistence of global solutions to a wave equation with a nonlinear memory term in a bounded domain. The proof of blow-up results is based on the eigenfunction method and the asymptotic properties of solutions for an ordinary fractional differential inequality.

math.AP↗