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This article is cited in 5 scientific papers (total in 5 papers)
Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonmonotonic nonlinearities
I. V. Denisova, A. I. Denisovb a Tula State Lev Tolstoy Pedagogical University, Tula, 300026 Russia
b National Research University Higher School of Economics, Moscow, 101000 Russia
Abstract:
For a singularly perturbed parabolic equation ${{\epsilon }^{2}}\left( {{{a}^{2}}\frac{{{{\partial }^{2}}u}}{{\partial {{x}^{2}}}} - \frac{{\partial u}}{{\partial t}}} \right) = F(u,x,t,\epsilon )$ in a rectangle, a problem with boundary conditions of the first kind is considered. At the corner points of the rectangle, the function $F$ is assumed to be quadratic and nonmonotonic with respect to the variable $u$ on the interval from the root of the degenerate equation to the boundary value. The main attention is paid to constructing the main term of the corner part of the asymptotics of the solution as $\epsilon\to0$ .
Key words:
boundary layer, asymptotic approximation, singularly perturbed equation.
Received: 02.04.2019 Revised: 02.04.2019 Accepted: 15.05.2019
Citation:
I. V. Denisov, A. I. Denisov, “Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonmonotonic nonlinearities”, Zh. Vychisl. Mat. Mat. Fiz., 59:9 (2019), 1581–1590; Comput. Math. Math. Phys., 59:9 (2019), 1518–1527
Linking options:
https://www.mathnet.ru/eng/zvmmf10956 https://www.mathnet.ru/eng/zvmmf/v59/i9/p1581
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Abstract page: | 132 | References: | 24 |
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