Dynamical Systems & Partial Differential Equations

Dear Colleagues,

This Special Issue gathers research at the interface of dynamical systems and partial differential equations (PDEs), emphasizing analysis, qualitative behavior, numerical methods, and applications in physics, engineering, biology, and data-driven modeling. Topics include well-posedness, stability and bifurcation, long-time dynamics and attractors, control and inverse problems, multiscale and nonlocal models, fractional and stochastic PDEs, PDE operators theory (e.g., p-Laplacian, bi-Laplacian, Porous Medium Equation, General Nonlinear Operators), and modern computational approaches (e.g., PINNs/operator learning) consistent with the journal’s scope in analysis of PDEs and dynamical systems.

Dynamical systems and partial differential equations provide a unified language to describe time-dependent and spatially distributed phenomena across the natural and engineering sciences. Advances in well-posedness, qualitative analysis, stability/bifurcation, and efficient computation have deepened our understanding of complex behavior from pattern formation and waves to turbulence, control, and inference. We are pleased to invite you to contribute to this Special Issue, which aims to showcase recent theoretical developments, computational techniques, and impactful applications at this intersection.

This Issue aims to advance the theory and applications of dynamical systems and PDEs based on analysis, computation, and cross-disciplinary applications.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

• Analysis of evolution PDEs: existence, uniqueness, regularity, blow-up, long-time dynamics, and attractors.
• Stability, bifurcation, chaos, and qualitative dynamics in ODE/PDE models (including low- and infinite-dimensional systems).
• Dispersive, hyperbolic, parabolic, and elliptic problems; conservation laws and nonlinear waves.
• Nonlocal, fractional, and stochastic PDEs; multiscale and heterogeneous media.
• Control, optimization, and inverse problems for dynamical systems and PDEs.
• Numerical analysis and scientific computing for PDE/dynamical systems (finite elements/differences/spectral; structure-preserving methods).
• Data-driven discovery and machine-learning methods for PDEs and dynamical systems (e.g., PINNs, operator learning).
• Applications in fluid mechanics, materials science, biology, epidemiology, control/robotics, and complex networks.

I look forward to receiving your contributions.

Prof. Dr. José Luis Díaz
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.

• dynamical systems
• evolution equations
• stability and bifurcation
• attractors
• nonlinear PDEs
• dispersive and hyperbolic equations
• parabolic/elliptic problems
• control and inverse problems
• fractional and stochastic PDEs
• numerical analysis
• data-driven and machine-learning methods for PDEs
• multiscale modeling
• applications in fluids, materials, and life science