Partial Differential Equations

Victor Henner, Alexander Nepomnyashchy, Tatyana Belozerova and Mikhail Khenner
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Victor Henner: Perm State University, Department of Physics
Alexander Nepomnyashchy: Israel Institute of Technology, Department of Mathematics
Tatyana Belozerova: Perm State University, Department of Mathematics
Mikhail Khenner: Western Kentucky University, Department of Mathematics

Chapter Chapter 13 in Ordinary Differential Equations, 2023, pp 479-545 from Springer

Abstract: Abstract In the previous chapters of this book, we have seen that the ODEs provide a mathematical formulation for various problems in mechanics, physics, and biology. Also, the ODEs serve as a powerful tool for solving mathematical problems, even when their initial formulation does not contain ODEs. In Chap. 12 , the application of ODEs in the variational analysis is demonstrated. In the present chapter, we consider a new class of mathematical problems, the partial differential equations (PDEs). Let us emphasize that this chapter cannot replace a comprehensive textbook on PDEs (see, e.g., [9]). Here, we are going to explain how definite classes of PDEs can be solved be their reduction to ODEs.

Date: 2023
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DOI: 10.1007/978-3-031-25130-6_13

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