Advertisement

Estimates for spatio-temporally dependent reaction diffusion systems

  • W. E. Fitzgibbon
  • J. J. Morgan
  • R. S. Sanders
  • S. J. Waggoner
Research Articles
  • 2.6k Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1475)

Keywords

Parabolic Equation Heat Kernel Global Existence Adjoint Equation Reaction Diffusion System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. 1.
    Amann H. (1986): Quasilinear evolution equations and parabolic systems. Trans. Amer. Math. Soc., Providence, 191–227zbMATHGoogle Scholar
  2. 2.
    Aronson, D.G. (1967): Bounds for the fundamental solution of a parabolic equation. Bulletin American Mathematical Society, 73, 890–896MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Aronson, D. G. (1968): Non-negative solutions of linear parabolic equations. Annali Scuola Norm. Sup. Pisa, 22, 607–694MathSciNetzbMATHGoogle Scholar
  4. 4.
    Farr, W., Fitzgibbon, W., Morgan, J., Waggoner, S.: Asymptotic convergence for a class of autocatalytic chemical reactions. Partial Differential Equations and Applications, Marcel Dekker, to appearGoogle Scholar
  5. 5.
    Fitzgibbon, W., Morgan, J., Waggoner, S. (1990): Generalized Lyapunov structure for a class of semilinear parabolic systems. JMAA, 152, 109–130MathSciNetzbMATHGoogle Scholar
  6. 6.
    Fitzgibbon, W., Morgan, J., Waggoner, S.: Weakly coupled semilinear parabolic evolution systems. Annali Mat. Pura Appl., to appearGoogle Scholar
  7. 7.
    Fitzgibbon, W., Morgan, J, Sanders, R.: Global existence and boundedness for a class of inhomogeneous semilinear parabolic systems. University of Houston, Technical Report UH/MD-87Google Scholar
  8. 8.
    Gray, P. and Scott, S. (1985): Sustained oscillations in a CSTR. J. Phys. Chem., 89, 22CrossRefGoogle Scholar
  9. 9.
    Henry, D., (1981): Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics 840, Springer Verlag, Berlin-Heidelberg-New YorkzbMATHGoogle Scholar
  10. 10.
    Hollis, S., (1986): Globally bounded solutions of reaction-diffusion systems. Dissertation, North Carolina State UniversityGoogle Scholar
  11. 11.
    Hollis, S., Martin, R., Pierre, M. (1987): Global existence and boundedness in reaction-diffusion systems. SIAM J. Math. Anal., 18, 744–761MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kanel, Y.I. (1984): Cauchy's problem for semilinear parabolic equations with balance conditions. Trans. Diff. Urav., 20, No. 10, 1753–1760MathSciNetzbMATHGoogle Scholar
  13. 13.
    Ladyzenskaja, O., Solonnikov, V., Uralceva, N. (1968): Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monograph 23, American Mathematical Society, ProvidenceGoogle Scholar
  14. 14.
    Morgan, J. (1990): Boundedness and decay results for reaction diffusion systems. SIAM J. Math Anal., to appearGoogle Scholar
  15. 15.
    Morgan, J. (1989): Global existence for semilinear parabolic systems. SIAM J. Math Anal., 20, No.5, 1128–1144MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Pazy, A. (1983): Semigroups of Linear Operations and Applications to Partial Differential Equations. Applied Mathematical Science, 44, Springer Verlag, Berlin-Heidelberg-New YorkCrossRefzbMATHGoogle Scholar
  17. 17.
    Waggoner, S. (1988): Global existence for solutions of semilinear and quasilinear parabolic systems of partial differential equations. Dissertation, University of HoustonGoogle Scholar
  18. 18.
    Haraux A., Youkana, A., (1988): On a Result of K. Masuda concerning reaction diffusion equations. Tohoku J. Math. 40, 159–183MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Singh, M., Khetarpal, K., Sharan (1980): A theoretical model for studying the rate of oxygenation of blood in pulmonary capillaries. J. Math Biology 9, 305–330CrossRefzbMATHGoogle Scholar
  20. 20.
    Feng, W. (1988): Coupled systems of reaction-diffusion equations and applications. Dissertation, North Carolina State UniversityGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • W. E. Fitzgibbon
  • J. J. Morgan
  • R. S. Sanders
  • S. J. Waggoner

There are no affiliations available

Personalised recommendations