Elliptic regularization for the heat equation with nonlinear boundary conditions

Asymptotic Analysis

Volumn 35, Issue 2, 2003, Pages 151-164

  Apreutesei, N C ^a   Volpert, V A ^b  

^a GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IASI   (Romania)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

Elliptic regularization; Maximal monotone operator; Singular perturbations

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; GRAPH THEORY; HEAT TRANSFER; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; PERTURBATION TECHNIQUES;

ASYMPTOTIC EXPANSION; BOUNDARY FUNCTION METHOD; ELLIPTIC REGULARIZATION; HEAT EQUATIONS; NONLINEAR BOUNDARY CONDITIONS;

NONLINEAR EQUATIONS;

EID: 0141508979     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. A.R. Aftabizadeh and N.H. Pavel, Boundary value problems for second order differential equations and a convex problem of Bolza, Differential Integral Equations 2 (1989), 495-509.
2. A.R. Aftabizadeh and N.H. Pavel, Nonlinear boundary value problems for some ordinary and partial differential equations associated with monotone operators, J. Math. Anal. Appl. 156 (1991), 535-557.
3. N.C. Apreutesei, An asymptotic analysis for a semilinear elliptic equation, Comm. Appl. Anal. 7(1) (2003), 67-77.
4. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976.
5. V. Barbu, Partial Differential Equations and Boundary value Problems, Kluwer Academic, Dordrecht, 1998.
6. H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. in: Contributions to Nonlinear Functional Analysis, E. Zarantonello, ed., Academic Press, 1971.
7. H. Brézis, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1992.
8. J.-L. Lions, Équations Différentielles Opérationnelles, Springer, 1961.
9. J.-L. Lions, Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal, Springer, Berlin, 1973.
10. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. 1, Springer, Berlin, 1972.
11. A. Vasilieva, V. Butuzov and L. Kalachev, The Boundary Function Method for Singular Perturbation Problems, SIAM, Philadelphia, 1995.
12. L. Véron, Problèmes d'évolution du second ordre associés à des opérateurs monotones, C. R. Acad. Sci. Paris 278 (1974). 1099-1101.
13. M. Vishik and L. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter multiplying the highest derivatives, Uspekhi Mat. Nauk 12 (1957), 3-122 (in Russian)
14. M. Vishik and L. Lyusternik, Regular degeneration and boyndary layer for linear differential equations with small parameter multiplying the highest derivatives, Amer. Math. Soc. Transl. Ser. 2 20 (1962), 239-364.
15. L.R. Volevich, The Vishik-Lyusternik method in general elliptic boundary value problems with small parameter, Preprint No. 26, Institute of Applied Mathematics, Moscow, 2002.