Abstract
In this paper, we consider a singularly perturbed problem of a kind of quasilinear hyperbolic-parabolic equations, subject to initial-boundary value conditions with moving boundary:
When certain assumptions are satisfied and ε is sufficiently small, the solution of this problem has a generalized asymptotic expansion (in the Van der Corput sense), which takes the sufficiently smooth solution of the reduced problem as the first term, and is uniformly valid in domain Q where the sufficiently smooth solution exists. The layer exists in the neighborhood of t=0. This paper is the development of references [3–5].
Similar content being viewed by others
References
Zlamal, M., On mixed problem for a hyperbolic equation with a small parameter,J. Math. Czechoslovakia 9, 94 (1959).
Jiang Fu-ru,Selected Works of the Mathematics Department of Fudan University (1962), 52. (in Chinese)
Gao Ru-xi, Singular perturbation for quasilinear hyperbolic equations,Chinese Annals of Mathematics,4B, 3 (1983), 293–298. (in Chinese)
Kang Lian-cheng, Singular perturbation for mixed problem of a kind of quasilinear hyperbolic-parabolic equation,Chinese Annals of Mathematics,6A, 6 (1985), 707–714. (in Chinese)
Kang Lian-cheng, On singular perturbation for a nonlinear initial-boundary value problem (I),Chinese Annals of Mathematics,10A, 5 (1989), 529–531. (in Chinese).
Jiang Fu-ru, On the boundary layer methods,Applied Mathematics and Mechanics (English Ed.).2, 5 (1981), 505–518.
Van der Corput, J.G., Asymptotic developments,J. Anal. Math.,4 (1955), 341–418.
Zhou Yu-lin, On boundary problem for nonlinear parabolic equation,Mathematics Proceedings,47, (89) 4 (1959), 431–484. (in Russian)
Xu Ke-ming, A kind of boundary value problem for nonlinear parabolic equations,Journal of Mathematical Research and Exposition,7, 2 (1987), 277–282. (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Dai Shi-qiang
The Project supported by the National Natural Science Foundation of China.
Rights and permissions
About this article
Cite this article
Lian-cheng, K. On singular perturbation for a nonlinear initial-boundary value problem (II). Appl Math Mech 13, 149–157 (1992). https://doi.org/10.1007/BF02454238
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02454238