Dear Colleagues,

This Special Issue of Mathematics (MDPI) on “Diffusion Equations and Models with Applications” invites both original and review manuscripts that bring together novel mathematical concepts and innovative computational methods for time-dependent diffusion models with real-life applications. Diffusion processes (linear and nonlinear) are crucial in various important phenomena in the life sciences, engineering, and environmental sciences. For example, when studying a mathematical model of a valve-regulated lead-acid battery under discharge or the sustained oscillations and spatial patterns that biological and biochemical systems produce or the transport of contaminants in waterbodies or a model of induction heating, one encounters diffusion and other related processes, such as advection, dispersion, reaction, and sorption. In population models, various forms of nonlinear diffusion can capture the effects of crowding or aggregation processes within species. 

Mathematical models in the form of time-dependent partial differential equations that have interplay between diffusion (whether linear or nonlinear) and other physical processes can produce fascinating solutions in the form of traveling waves or target patterns or even solutions that blow up in finite time. Further, if one is to recover the transport history of a contaminant, one has to analyze backward-diffusion and, thus, an ill-posed problem. The purpose of this Special Issue is to gather contributions from experts who are working on a variety of interesting time-dependent diffusion-related partial differential equation models in the life sciences, engineering, and environmental sciences. The contributions can be for models that describe either initial value problems or initial boundary value problems. Moreover, time-dependent models can be either forward in time or backward in time. Innovative computational studies of models that exploit and corroborate known theoretical results of the models are welcome. 

Prof. Dr. Valipuram S. Manoranjan
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.

• diffusion-related models
• time-dependent partial differential equations
• initial value problems
• initial boundary value problems
• applications in the life sciences, engineering, and environmental sciences