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 12
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
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- nonlinear elliptic and parabolic equations
- nonlocal operators
- chemotaxis models
- fluid equations
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.
Further information on MDPI's Special Issue policies can be found here.
