|| Special Issue || Qualitative Theory of Partial Differential Equations and Applications
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Deadline for Submissions: 20 January 2024 |
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Special Issue Editors |
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Guest Editor |
Assoc. Prof. Jun Zheng |
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Affiliation |
1. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China 2. Department of Electrical Engineering, Polytechnique Montréal, Montreal H3T 1J4, Canada |
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Interests |
regularity theory of PDEs; free boundary problems; control theory and applications; nonlinear functional analysis | |||
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Guest Editor |
Assoc. Prof. Wulong Liu |
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Affiliation |
School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China | |||
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Interests |
variational methods; nonlinear problems in physics and geome | |||
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Guest Editor |
Prof. Leandro S. Tavares |
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Affiliation |
Centro de Ciências e Tecnologia, Universidade Federal do Cariri, Juazeiro do Norte-CE 63048-080 Brazil | |||
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Interests |
regularity theory of PDEs; elliptic PDEs; free boundary problems; variational methods; bifurcation theory; topological methods | |||
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Guest Editor |
Prof. Alânnio B. Nóbrega | Website |
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Affiliation |
Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, PB 58429-900 Brazil | |||
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Interests |
elliptic PDEs; variational methods; bifurcation theory; topological methods; nonlocal problems | |||
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Special Issue Information |
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In the natural world, many dynamics can be modeled by partial differential equations (PDEs), such as reaction diffusion motion, chemical reaction and phase transition, fluid motion, and wave propagation, to name a few. According to the needs of specific problems, it is necessary to study existence (or non-existence) and properties of solutions to the PDEs from different perspectives.
This special issue will bring together experts of pure mathematics, applied mathematics and interdisciplines to discuss fundamental problems that are related to PDEs, and practical applications of PDEs in various fields. It is dedicated to the presentation of qualitative theory of PDEs either at a theoretical level or at a level of their multiple applications to sciences, e.g., mathematical physics, chemistry, biology, engineering, etc.
Researchers, who are interested in submitting an article to this special issue, are encouraged to address new equations or models, new techniques, new analysis tools, novel ideas, or practical applications, etc.
In particular, articles in the following areas are most welcome: · non-existence, existence, and uniqueness or multiplicity of solutions · regularity of solutions, e.g., boundedness, continuity, integrability, differentiability, etc. · properties of solutions, e.g., symmetry, nondegeneracy, nonnegativity, concentration, monotonicity, conservation law, etc. · characterizations on parameters/data, e.g., continuous dependence of solutions on initial data, homogenization, bifurcation, etc. · geometric properties of level sets or free boundaries, e.g., porosity, Hausdorff measure, star-shapedness, etc. · behavior of solutions at finite or long time, e.g., stability (in various sense), extinction, blow-up, periodicity, etc. · stabilization of PDE systems with anti-stable terms · control theory of PDE systems, e.g., controllability, observability, Lyapunov characterizations, etc. · PDE control in practical problems, e.g., establishment of a PDE model, control design, stability analysis, simulations, etc. · important inequalities and theorems involved in PDEs, e.g., Harnack’ inequality, Caffarelli-Kohn-Nirenberg’s inequality, comparison principle, monotonicity formula, etc. |
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Published Papers |
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This special issue is now open for submission. |
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