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This article is cited in 3 scientific papers (total in 3 papers)
Mathematical physics
Corner boundary layer in boundary value problems with nonlinearities having stationary points
I. V. Denisov Tula State Lev Tolstoy Pedagogical University, 300026, Tula, Russia
Abstract:
For a singularly perturbed parabolic equation
$$
\varepsilon^2\biggl(a^2\frac{\partial^2u}{\partial x^2}-\frac{\partial u}{\partial t}\biggr)=F(u,x,t,\epsilon)
$$
in a rectangle, a problem with boundary conditions of the first kind is considered. It is assumed that, at the corner points of the rectangle, the function $F$ is cubic in the variable $u$. The zero of the derivative of $F$ and the boundary value of the problem at each corner point of the rectangle lie on one side of the solution of the degenerate equation. A complete asymptotic expansion of the solution at $\varepsilon\to0$ is constructed, and its uniformity in the closed rectangle is substantiated.
Key words:
boundary layer, asymptotic approximation, singularly perturbed equation.
Received: 16.06.2020 Revised: 21.07.2020 Accepted: 07.07.2021
Citation:
I. V. Denisov, “Corner boundary layer in boundary value problems with nonlinearities having stationary points”, Zh. Vychisl. Mat. Mat. Fiz., 61:11 (2021), 1894–1903; Comput. Math. Math. Phys., 61:11 (2021), 1855–1863
Linking options:
https://www.mathnet.ru/eng/zvmmf11320 https://www.mathnet.ru/eng/zvmmf/v61/i11/p1894
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