1.个人简介：

常彩虹，女，副教授，硕士生导师。2022年12月毕业于西安交通大学数学专业，获理学博士学位，美国圣母大学应用数学系联合培养博士生。长期致力于非线性偏微分方程理论及其应用等相关领域的研究工作。近年来，主持国家自然科学基金青年基金项目、陕西省自然科学基础研究计划项目各一项，参与国家自然科学基金面上项目一项。已第一作者或通讯作者在Journal of Differential Equations，Nonlinear Analysis. Theory, Methods & Applications，Proceedings of the Royal Society of Edinburgh Section A: Mathematics，Discrete and Continuous Dynamical Systems. Series A等学术期刊上发表SCI论文10余篇。目前担任Nonlinear Analysis: Real World Application，Discrete and Continuous Dynamical Systems. Series B等国际学术期刊审稿人。

2.学习工作经历：

  2024.12至今，西安科技大学，理学院，副教授

  2023.03至2024.11，西安科技大学，理学院，讲师

  2021.09至2022.09，美国圣母大学，应用数学系，联合培养博士生

  2018.09至2022.12，西安交通大学，数学与统计学院，博士研究生

3.研究方向：

1. 非线性椭圆型、抛物型方程解的适定性与渐近性

2. 真菌感染模型自由边界问题

    

   4.主持项目：

3. 国家自然科学基金青年基金项目：含非线性梯度乘积项的椭圆型方程的Liouville型定理及其应用，30万，2025.01-2027.12，主持，在研。

4. 陕西省科技厅一般项目（青年）：带非线性梯度项的退化椭圆方程解的存在性研究，5万，2024.01-2025.12，主持，在研。

5. 西安科技大学高层次人才引进科研启动经费，30万，2023.03至今，主持，在研。

6. 国家自然科学基金面上项目：几类梯度项超临界增长抛物方程的定性研究，44万，2027.01-2030.12，参与，在研。

7. 国家自然科学基金面上项目：辐射流体力学方程组渐近极限的数学理论研究，51万，2021.01-2024.12，参与，结题。

    

   5.代表性论文：

8. Chang CH, Zhang ZC, Hu B. Analysis of a free boundary problem modeling immune response to fungal infection in multi-space dimensional case. Journal of Differential Equations, 2026, 453: 113857.

   [2] Chang CH, Zhang ZC. A priori estimates and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms. Nonlinear Analysis, 2026, 267: 114064.

   [3] Chang CH, Zhang ZC. Liouville-type theorem for Einstein-scalar field Lichnerowicz-type equation. Journal of Mathematical Analysis and Applications, 2026, 561: 130659.

   [4] Chang CH, Zhang ZC. Liouville-type theorems for the quasilinear elliptic equation and inequality with logarithmic nonlinearity. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2025. 1-16.

   [5] Chang CH, Yang JZ. The Constitutive Equation-Based Recrystallization Mechanism of Ti-6Al-4V Alloy during Superplastic Forming. Coatings, 2024, 14: 122.

   [6] Liu JY, Wang B, Chang CH. Asymptotic Behavior of Singular Solution to the k-Hessian Equation with a Matukuma-Type Source. Wuhan University Journal of Natural Sciences, 2024, 29: 242-256.

   [7] Chang CH, Hu B, Zhang ZC. Gradient blowup behavior for a viscous Hamilton-Jacobi equation with degenerate gradient nonlinearity. Journal of Differential Equations, 2023, 359: 23-66.

   [8] Chang CH, Hu B, Zhang ZC. Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms. Nonlinear Analysis. Theory, Methods & Applications, 2022, 220: 112873.

   [9] Chang CH, Zhang ZC. Asymptotic behavior of blowup solutions to the semilinear heat equation with weighted exponential reaction term. Electronic Journal of Differential Equations, 2022, 2022: 42.

   [10] Chang CH, Ju QC, Zhang ZC. Asymptotic behavior of global solutions to a class of heat equations with gradient nonlinearity. Discrete and Continuous Dynamical Systems. Series A, 2020, 40: 5991-6014.

   [11] Li FY, Chang CH, Feng XJ. Existence of solutions to a class of Schrödinger-Poisson systems with indefinite nonlinearity. Applicable Analysis. 2017, 96: 721-740.