Abstract:
This paper investigates a two-point boundary value problem for a second-order singularly perturbed ordinary differential equation in the case of multiple roots of the degenerate equation. This is a new class of problems, namely, problems with discontinuous nonlinear terms on the right-hand side of the equation, which leads to the formation of a multizonal interior transitional layer in a neighborhood of the discontinuity point. For sufficiently small parameter values, the existence of a smooth solution is proved, and its asymptotic expansion is constructed, showing that this solution qualitatively differs from the case when the degenerate equation has simple roots.
This work is supported by the National Natural Science Foundation of China (no. 11871217) and the Science and Technology Commission of Shanghai Municipality (no. 18dz2271000). The corresponding author is Mingkang Ni.
This publication is cited in the following 4 articles:
Qian Yang, Mingkang Ni, “Multizonal Internal Layers in a Stationary Piecewise–Smooth Reaction-Diffusion Equation in the Case of the Difference of Multiplicity for the Roots of the Degenerate Solution”, Comput. Math. and Math. Phys., 64:5 (2024), 1130
Qian Yang, Mingkang Ni, “Multiscale study on a class of singularly perturbed system with discontinuous right-hand side and multiple root of the degenerate solution”, Communications in Nonlinear Science and Numerical Simulation, 139 (2024), 108247
Q. Yang, M. Ni, “Multizonal boundary and internal layers in the singularly perturbed problems for a stationary equation of reaction–advection–diffusion type with weak and discontinuous nonlinearity”, Comput. Math. Math. Phys., 62:12 (2022), 2123–2138
Qian Yang, Mingkang Ni, “ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION”, jaac, 12:6 (2022), 2441