Nonlinear Elliptic Partial Differential Equations: Theory, Computations, and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".
Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 217
Special Issue Editors
Interests: partial differential equations; nonlinear elliptic boundary value problems; reaction diffusion equations; mathematical ecology
Special Issue Information
Dear Colleagues,
Partial differential equations (PDEs) and boundary value problems (BVPs) provide a mathematical framework for describing natural phenomena. Mathematically understanding the properties of solutions to PDEs and BVPs while also being able to use computers to approximate the unknown solution(s) reliably and efficiently has become an invaluable tool for describing and understanding the physical world. As numerical techniques have evolved alongside improving computing technology, new analytic techniques have been discovered, and more sophisticated mathematical models using PDEs have been developed, there has been an ever-expanding need to both theoretically and computationally understand PDEs and BVPs. Theoretical results inspire computational research, and computational results help to build the understanding of PDEs and BVPs. An interdisciplinary approach to PDEs and BVPs naturally evolves both the numerical analysis and the theoretical analysis required to understand the expansive applications and the elegant mathematics linked to PDEs and BVPs.
We welcome submissions that advance the theoretical understanding of the class of nonlinear elliptic PDEs and BVPs. We also welcome submissions that formulate and analyze computational methods for approximating solutions to nonlinear elliptic problems—in particular, the rigorous study of convergence, admissibility, accuracy, and/or stability results or the formulation of highly efficient implementations and/or highly accurate methods for approximating application problems.
Prof. Dr. Ratnasingham Shivaji
Dr. Tom Lewis
Guest Editors
Manuscript Submission Information
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Keywords
- reaction diffusion equations
- existence/multiplicity/uniqueness
- regularity
- stability
- boundary value problems
- nonlinear elliptic equations
- numerical PDEs
- convergence analysis
