Recent Developments in Partial Differential Equations and Their Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".
Deadline for manuscript submissions: 30 June 2026 | Viewed by 1165
Special Issue Editor
Interests: nonlinear elliptic and parabolic equations; nonlocal operators; chemotaxis models; fluid equations
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The classical Keller–Segel model describes chemotaxis, a biological process in which cells migrate toward higher concentrations of a chemical signal. Chemotaxis and its variant system have been extensively studied in recent years. In investigating the long-time behavior of Keller–Segel systems, we focus on models with general nonlinear dependence of diffusion and cross-diffusion rates on population density. To address the challenges posed by nonlinear terms, we construct a proper Lyapunov and employ a tailored Moser iteration, in which the time variable is continuously postponed during the iteration process. This method can be extended to the attraction–repulsion system, haptotaxis system, and related models.
In addition, I am particularly interested in the interplay between boundary geometric properties and boundary regularity across various classes of parabolic equations, including linear equations, p-Laplace equations, and fractional Laplace equations. This line of inquiry underscores the profound connection between 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
- nonlinear elliptic and parabolic equations
- nonlocal operators
- chemotaxis models
- fluid equations
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