On a class of parabolic equations with nonlocal boundary conditions

Journal of Mathematical Analysis and Applications

Volumn 294, Issue 2, 2004, Pages 712-728

  Yin, Hong Ming ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Ion transport model; Nonlocal boundary conditions; Reaction diffusion equations

Indexed keywords

EID: 3142677183     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.03.021     Document Type: Article

References (20)

1. Chadam J.M. Yin H.-M. A diffusion equation with localized reactions Proc. Edinburgh Math. Soc. 37 1994 101-118
2. Day W.A. A decreasing property of solution of a parabolic equation with applications to thermoelasticity Quart. Appl. Math. 40 1982 319-330
3. Day W.A. Heat Conduction within Linear Thermoelasticity 1985 Springer-Verlag New York
4. 1 cylinders Proc. Sympos. Pure Math. 35 1979 179-196
5. Friedman A. Monotonic decay of solution of parabolic equations with nonlocal boundary conditions Quart. Appl. Math. 44 1986 401-407
6. Friedman A. Partial Differential Equations of Parabolic Type 1983 Krieger Malabar, FL
7. Lieberman G. Second Order Parabolic Differential Equations 1996 World Scientific Singapore
8. Ladyzenskaja O.A. Solonnikov V.A. Ural'ceva N.N. Linear and Quasi-Linear Equations of Parabolic Type Amer. Math. Soc. Transl., vol. 23 1968 American Mathematical Society Providence, RI
9. Lin Y. Xu S. Yin H.-M. Finite difference approximation for a class of nonlocal parabolic equations Internat. J. Math. Math. Sci. 20 1997 147-164
10. Levitt D.G. Interpretation of biological ion channel flux data: reaction rate versus continuum theory Annu. Rev. Biophys. Biophys. Chem. 15 1986 29-57
11. Mazja V.G. Sobolev Spaces 1985 Springer-Verlag New York
12. McGill P. Schumaker M.F. Boundary conditions for single-ion diffusion Biophys. J. 71 1996 1723-1742
13. E. Mapes, M.F. Schumaker, Time-dependent boundary conditions for single-ion diffusion, preprint
14. Pao C.V. Nonlinear Parabolic and Elliptic Equations 1992 Plenum New York
15. Pao C.V. Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions J. Math. Anal. Appl. 195 1995 702-718
16. Pao C.V. Dynamics of reaction-diffusion equations with nonlocal boundary conditions Quart. Appl. Math. 53 1995 173-186
17. Pao C.V. Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions J. Comput. Appl. Math. 88 1998 225-238
18. Pao C.V. Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions J. Comput. Appl. Math. 136 2001 227-243
19. Schumaker M.F. Boundary conditions and trajectories of diffusion processes J. Chem. Phys. 117 2002 2469-2473
20. Carl S. Lakshmikantham V. Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions J. Math. Anal. Appl. 217 2002 182 205