Bukzhalev, E. E.; Vasil’eva, A. B. Solutions to a singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders. (Russian, English) Zbl 1210.35015 Zh. Vychisl. Mat. Mat. Fiz. 47, No. 3, 424-437 (2007); translation in Comput. Math. Math. Phys. 47, No. 3, 407-419 (2007). Summary: The solution to a singularly perturbed parabolic equation with internal and boundary layers whose stretched variables may depend on different powers of the perturbation parameter is considered. An asymptotic representation of the solution is constructed and substantiated, and its stability is proved. Cited in 1 Document MSC: 35B20 Perturbations in context of PDEs Keywords:singular perturbations; step-like contrasting structures; method of boundary functions; differential inequalities method; parabolic equations solution stability PDFBibTeX XMLCite \textit{E. E. Bukzhalev} and \textit{A. B. Vasil'eva}, Zh. Vychisl. Mat. Mat. Fiz. 47, No. 3, 424--437 (2007; Zbl 1210.35015); translation in Comput. Math. Math. Phys. 47, No. 3, 407--419 (2007) Full Text: DOI