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Estimates for spatio-temporally dependent reaction diffusion systems

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Delay Differential Equations and Dynamical Systems

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Bibliography

  1. Amann H. (1986): Quasilinear evolution equations and parabolic systems. Trans. Amer. Math. Soc., Providence, 191–227

    MATH  Google Scholar 

  2. Aronson, D.G. (1967): Bounds for the fundamental solution of a parabolic equation. Bulletin American Mathematical Society, 73, 890–896

    Article  MathSciNet  MATH  Google Scholar 

  3. Aronson, D. G. (1968): Non-negative solutions of linear parabolic equations. Annali Scuola Norm. Sup. Pisa, 22, 607–694

    MathSciNet  MATH  Google Scholar 

  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 appear

    Google Scholar 

  5. Fitzgibbon, W., Morgan, J., Waggoner, S. (1990): Generalized Lyapunov structure for a class of semilinear parabolic systems. JMAA, 152, 109–130

    MathSciNet  MATH  Google Scholar 

  6. Fitzgibbon, W., Morgan, J., Waggoner, S.: Weakly coupled semilinear parabolic evolution systems. Annali Mat. Pura Appl., to appear

    Google Scholar 

  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-87

    Google Scholar 

  8. Gray, P. and Scott, S. (1985): Sustained oscillations in a CSTR. J. Phys. Chem., 89, 22

    Article  Google Scholar 

  9. Henry, D., (1981): Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics 840, Springer Verlag, Berlin-Heidelberg-New York

    MATH  Google Scholar 

  10. Hollis, S., (1986): Globally bounded solutions of reaction-diffusion systems. Dissertation, North Carolina State University

    Google Scholar 

  11. Hollis, S., Martin, R., Pierre, M. (1987): Global existence and boundedness in reaction-diffusion systems. SIAM J. Math. Anal., 18, 744–761

    Article  MathSciNet  MATH  Google Scholar 

  12. Kanel, Y.I. (1984): Cauchy's problem for semilinear parabolic equations with balance conditions. Trans. Diff. Urav., 20, No. 10, 1753–1760

    MathSciNet  MATH  Google Scholar 

  13. Ladyzenskaja, O., Solonnikov, V., Uralceva, N. (1968): Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monograph 23, American Mathematical Society, Providence

    Google Scholar 

  14. Morgan, J. (1990): Boundedness and decay results for reaction diffusion systems. SIAM J. Math Anal., to appear

    Google Scholar 

  15. Morgan, J. (1989): Global existence for semilinear parabolic systems. SIAM J. Math Anal., 20, No.5, 1128–1144

    Article  MathSciNet  MATH  Google Scholar 

  16. Pazy, A. (1983): Semigroups of Linear Operations and Applications to Partial Differential Equations. Applied Mathematical Science, 44, Springer Verlag, Berlin-Heidelberg-New York

    Book  MATH  Google Scholar 

  17. Waggoner, S. (1988): Global existence for solutions of semilinear and quasilinear parabolic systems of partial differential equations. Dissertation, University of Houston

    Google Scholar 

  18. Haraux A., Youkana, A., (1988): On a Result of K. Masuda concerning reaction diffusion equations. Tohoku J. Math. 40, 159–183

    Article  MathSciNet  MATH  Google Scholar 

  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, 305–330

    Article  MATH  Google Scholar 

  20. Feng, W. (1988): Coupled systems of reaction-diffusion equations and applications. Dissertation, North Carolina State University

    Google Scholar 

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Authors

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Stavros Busenberg Mario Martelli

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© 1991 Springer-Verlag

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Fitzgibbon, W.E., Morgan, J.J., Sanders, R.S., Waggoner, S.J. (1991). Estimates for spatio-temporally dependent reaction diffusion systems. In: Busenberg, S., Martelli, M. (eds) Delay Differential Equations and Dynamical Systems. Lecture Notes in Mathematics, vol 1475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083486

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  • DOI: https://doi.org/10.1007/BFb0083486

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54120-2

  • Online ISBN: 978-3-540-47418-0

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