Advances in Nonlinear Elliptic and Parabolic Equations
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".
Deadline for manuscript submissions: 31 August 2025 | Viewed by 897
Special Issue Editor
Special Issue Information
Dear Colleagues,
My research interests are nonlinear elliptic and parabolic equations, nonlocal operators, chemotaxis models, and fluid equations.
The classical Keller–Segel model describes a biological process, chemotaxis, in which cells migrate towards higher concentrations of a chemical signal, and chemotaxis and its variant system have been studied extensively in recent years. When studying the large-time behaviors for Keller–Segel systems, we focus on the models with quite general nonlinear dependence of diffusion and cross-diffusion rates on the population density. In order to solve the difficulty caused by nonlinear terms, we construct a proper Lyapunov and utilize a designed Moser iteration, in which the time variable is continuously postponed while performing the iteration process. This method can be extended to the attraction-repulsion system, haptotaxis system, and so on.
I am also intrigued by the exploration of the intricate connection between boundary geometric properties and boundary regularity across various classes of parabolic equations, encompassing linear equations, p-Laplace equations, and fractional Laplace equations. This pursuit delves into the ultimate interplay of mathematical abstraction and real-world applications, highlighting the diverse manifestations of boundary behavior in these distinct mathematical contexts.
Dr. Mengyao Ding
Guest Editor
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Keywords
- chemotaxis models
- p-Laplacian
- nonlocal operators
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