|
|
|
References
|
|
|
1. |
M. S. Agranovich, M. I. Vishik, “Elliptic problems with a parameter and parabolic problems of general type”, Uspekhi Mat. Nauk, 19:3 (1964), 53–161 (in Russian) |
2. |
A. Antoniouk, N. Tarkhanov, The Dirichlet problem for the heat equation in domains with cuspidal points on the boundary, Operator Theory: Advances and Applications, Birkhäuser, Basel et al., 2012 |
3. |
V. N. Aref'ev, L. A. Bagirov, “Asymptotic behavior of solutions of the Dirichlet problem for a parabolic equation in domains with singularities”, Mat. Zam., 59:1 (1996), 12–23 (in Russian) |
4. |
G. D. Birkhoff, “On the asymptotic character of the solutions of certain linear differential equations containing a parameter”, Trans. Amer. Math. Soc., 9 (1908), 219–231 |
5. |
L. Boutet de Monvel, “Boundary problems for pseudo-differential operators”, Acta Math., 126:1–2 (1971), 11–51 |
6. |
A. S. Demidov, “Asymptotic behaviour of the solution of a boundary value problem for elliptic pseudodifferential equations with a small parameter multiplying the highest operator”, Trans. Moscow Math. Soc., 32 (1975), 119–146 |
7. |
G. I. Eskin, “Asymptotics of solutions of elliptic pseudodifferential equations with a small parameter”, Soviet Math. Dokl., 14:4 (1973), 1080–1084 |
8. |
G. I. Eskin, Boundary Value Problems for Elliptic Pseudodifferential Equations, Amer. Math. Soc., Providence, RI, 1980 |
9. |
L. S. Frank, Spaces and Singular Perturbations on Manifolds without Boundary, North Holland, Amsterdam, 1990 |
10. |
K. Friedrichs, “Asymptotic phenomena in mathematical physics”, Bull. Amer. Math. Soc., 61 (1955), 485–504 |
11. |
M. Gevrey, “Sur les équations partielles du type parabolique”, J. Math. pure appl. Paris, 9 (1913), 305–471; 10 (1914), 105–148 |
12. |
W. M. Greenlee, “Rate of convergence in singular perturbations”, Ann. Inst. Fourier (Grenoble), 18:2 (1968), 135–191 |
13. |
D. Huet, “Phénomènes de perturbation singulière dans les problèmes aux limites”, Ann. Inst. Fourier (Grenoble), 11 (1961), 385–475 |
14. |
A. M. Il'in, Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, Amer. Math. Soc., Providence, RI, 1992 |
15. |
A. I. Karol', “Operator-valued pseudodifferential operators and the resolvent of a degenerate elliptic operator”, Mat. Sb., 121(163):4 (1983), 562–575 |
16. |
J. Kevorkian, J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, Berlin–New York, 1981 |
17. |
V. A. Kondrat'ev, “Boundary problems for parabolic equations in closed domains”, Trans. Moscow Math. Soc., 15 (1966), 400–451 |
18. |
E. F. Mishchenko, N. Kh. Rozov, Differential Equations with Small Parameter and Relaxation Oscillations, Plenum Press, New York, 1980 |
19. |
S. A. Nazarov, “Vishik–Lyusternik method for elliptic boundary value problems in domains with conical points. I–III”, Sib. Mat. Zh., 22:4 (1981), 142–163 ; 22:5 (1981), 132–152 ; 25:6 (1984), 106–115 (in Russian) |
20. |
A. L. Pereira, M. C. Pereira, “An eigenvalue problem for the biharmonic operator on $\mathbb{Z}_2$-symmetric regions”, J. Lond. Math. Soc., 77:2 (2008), 424–442 |
21. |
H. Poincaré, “Sur les intégrales irrégulières des équations linéaires”, Acta Math., 8 (1886), 295–344 |
22. |
L. Prandtl, “Über Flüssigkeitsbewegung bei kleiner Reibung”, Verhandl. III. Int. Math.-Kongresses, Teubner, Leipzig, 1905, 484–491 |
23. |
V. Rabinovich, B.-W. Schulze, N. Tarkhanov, “A calculus of boundary value problems in domains with non-Lipschitz singular points”, Math. Nachr., 215 (2000), 115–160 |
24. |
I. B. Simonenko, “A new general method for investigating linear operator equations of the singular integral operator type. I; II”, Izv. Akad. Nauk SSSR, Ser. Mat., 29 (1965), 567–586 ; 757–782 (in Russian) |
25. |
M. I. Vishik, L. A. Lyusternik, “Regular degeneration and boundary layer for linear differential equations with small parameter”, Uspekhi Mat. Nauk, 12:5 (77) (1957), 3–122 (in Russian) |
26. |
L. R. Volevich, “The Vishik–Lyusternik method in elliptic problems with small parameter”, Trans. Moscow Math. Soc., 67 (2006), 87–125 |
27. |
W. Wasow, Asymptotic expansions for ordinary differential equations, Wiley, 1966 |