On unique solvability of nonlocal drift-diffusion-type problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 56, Issue 6, 2004, Pages 803-830

  Gajewski, H ^a   Skrypnik, I V ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b INSTITUTE OF APPLIED MATHEMATICS AND MECHANICS   (Ukraine)

Author keywords

Bounded solutions; Degenerate type; Nonlinear parabolic equations; Nonlocal drift; Nonstandard assumptions; Uniqueness

Indexed keywords

BOUNDARY VALUE PROBLEMS; ELECTROSTATICS; ESTIMATION; INTEGRATION; INTERPOLATION; MATHEMATICAL MODELS; PROBLEM SOLVING; SEMICONDUCTOR MATERIALS; THEOREM PROVING; THERMODYNAMICS; VECTORS;

BOUNDED SOLUTIONS; DEGENERATE TYPES; NONLINEAR PARABOLIC EQUATIONS; NONLOCAL DRIFTS; NONSTANDARD ASSUMPTIONS; UNIQUENESS;

NONLINEAR EQUATIONS;

EID: 0742268520     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2003.10.014     Document Type: Article

References (17)

1. Albinus G., Gajewski H., Hünlich R. Thermodynamic design of energy models of semiconductor devices. Nonlinearity. 15:2002;367-383.
2. Alt H.W., Luckhaus S. Quasilinear elliptic-parabolic differential equations. Math. Z. 183:1983;311-341.
3. Benilan Ph., Wittbold P. On mild and weak solutions of elliptic-parabolic systems. Adv. Differential Equations. 1:1996;1053-1073.
4. Elliot C.M., Garcke H. On the Cahn-Hilliard equation with degenerate mobility. SIAM J. Math. Anal. 27:1996;404-423.
5. Gajewski H. On a nonlocal model of nonisothermal phase separation. Adv. Math. Sci. Appl. 12:2002;569-586.
6. Gajewski H., Gröger K. Reaction-diffusion processes of electrically charged species. Math. Nachr. 177:1996;109-130.
7. Gajewski H., Skrypnik I.V. On the uniqueness of solutions for nonlinear elliptic-parabolic equations. J. Evolution Equations. 3:2003;247-281.
8. Gajewski H., Skrypnik I.V. To the uniqueness problem for nonlinear elliptic equations. Nonlinear Anal. 52:2003;291-304.
9. Gajewski H., Skrypnik I.V. On the uniqueness of solutions for nonlinear parabolic equations. Discrete Continuous Dyn. Systems. 10:2004;215-236.
10. Gajewski H., Zacharias K. Global behavior of a reaction-diffusion system modelling chemotaxis. Math. Nachr. 195:1998;77-114.
11. Gajewski H., Zacharias K. On a nonlocal phase separation model. J. Math. Anal. Appl. 286:2003;11-31.
12. Giacomin G., Lebowitz J.L. Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits. J. Statist. Phys. 87(1-2):1997;37-61.
13. Giacomin G., Lebowitz J.L. Phase segregation dynamics in particle systems with long range interactions. II. Interface motion. SIAM J. Appl. Math. 58(6):1998;1707-1729.
14. Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N. Linear and quasilinear equations of parabolic type. Translations of Mathematical Monographs. Vol. 23:1974;American Mathematical Society, Providence RI.
15. Littman W., Stampacchia G., Weinberger H.F. Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola Norm. Sup. Pisa. 17(3):1963;43-77.
16. 1 -contraction and uniqueness for quasilinear elliptic-parabolic equations C.R. Acad. Sci. Paris. 318(1):1995;1005-1010.
17. Skrypnik I.V. Methods for analysis of nonlinear elliptic boundary value problems. Translations of Mathematical Monographs. Vol 139:1994;American Mathematical Society, Providence, RI. xii+348pp.