JADEs Issue #7: Biharmonic PDE
In this issue, we explore the linear elliptic homogeneous fourth order Biharmonic equation: We start with the following definition first according to G.E. Shilov et al, Mathematical Analysis: A Special Course, Pergamon (1965).
PROBLEM
Definition
Given the desired function and its derivative along the normal are prescribed on the boundary:
We get the following general solution u(x,y):
Example 1
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Example 2
ABOUT THE JOURNAL
The Journal of Applied Differential Equations, otherwise known as JADEs is a free Open Access (OA) journal or e-journal (ISSN# pending) that covers both linear and nonlinear partial differential equations (PDEs) and ordinary differential equations (ODEs) and the analytic methods/solutions to these.
While most journals and proceedings take a very theory-driven real and/or complex analysis approach to PDEs and ODEs, this journal will discuss and illustrate problems from a very pragmatic, workshop problem-solution focus for applied/industrial mathematicians, scientists (physicists, chemists, etc.), engineers (mechanical, electrical, maybe some structural), and others who are actively solving problems in their domains.
Please subscribe if you want to see more problems like the ones above as well as other more relevant PDEs and/or ODEs with applications in mechanics (analytical, classical, Newtonian), electromagnetic field/quantum-based wave mechanics, fluid mechanics and beyond. Enjoy!
ABOUT THE EDITOR
Steve Anglin, M.Sc. Ph.D. (h.c.) is an applied, industrial mathematician primarily teaching and solving partial differential equations (PDEs) with applications in the fields of fluid mechanics (mechanical engineering) as well as some electrical engineering and physics. He is a former lecturer of mathematics at Case and Saint Leo Universities. Steve received his Master of Science (M.Sc.) in applied mathematics from Brown University (Ivy League) and his Hon. Doctorate (Ph.D.(h.c.)) in mathematics from Trinity College. Previously, he published or has been credited on 2,000+ technical trade books with Springer Nature and Pearson Education as well as 2 eZines with O'Reilly Media.
For more, visit:?https://www.amazon.com/author/steveanglin
Email:?[email protected]
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1 年This is an intriguing topic! It's amazing to witness the marriage of mathematics and engineering to solve complex PDEs. I'm especially impressed by the institutions involved in this research such as ICERM, MSRI, and MIT CSAIL. It makes me wonder what other areas of mathematics they are researching and how this could potentially be applied to other areas of physics and engineering. What do you think?