Bakhyt Alipova, University of Kentucky
2023 AWM Research Symposium
Panels, Roundtables, and Other Events

The "Mathematical modeling of Equations of Mathematical Physics" is applicable everywhere! Application of differential equations for solution of different applied problems of STEM is difficult to overestimate. We will discuss all stages of solution of boundary value problem:
- the basic concepts of operational calculus and the application of the Laplace transform (operational method) to the solution of various classes of differential and integral equations,
- the concepts of canonical forms for linear second-order hyperbolic equations, parabolic and elliptic types,
- the derivation of equations and boundary conditions describing various physical processes (f.e. heat propagation, substances in various media, stationary thermal and diffusion processes, etc.),
- at least, classification and formulation of boundary value problems are also considered here.
Problems on the properties of harmonic functions and the simplest boundary problems for the Laplace and Poisson equations are considered also. We could discuss the most common analytical methods for solving boundary value problems of mathematical physics: the d'Alembert method, the method of separation of variables (the Fourier method, the method of eigenfunctions), the methods of Fourier and Laplace integral transformations. It would be the Discussion for everybody who is finding application of their equations!

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