Estimates for spatio-temporally dependent reaction diffusion systems

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


Parabolic Equation Heat Kernel Global Existence Adjoint Equation Reaction Diffusion System 
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  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

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