References
Turing, A. M., The chemical basis of morphogenesis. Phil. Trans. Roy Soc. London, Series B 237, 37–72 (1952)
Othmer, H. G., & L. E. Scriven, Interactions of reaction and diffusion in open systems. I & EC Fund. 8, (2) 302–313 (1969)
Gmitro, J. I., & L. E. Scriven, A Physiochemical Basis for Pattern and Rhythm, pp. 221–255 in Intracellular Transport, K. B. Warren, ed. New York: Academic Press 1966
Gavalas, G. R., On the steady states of distributed parameter systems with chemical reactions, heat and mass transfer. Chem. Eng. Sci. 21, 477–492 (1966)
Wei, J., The stability of a reaction with intraparticle diffusion of mass and heat. The Lyapunov methods in metric function space. Chem. Eng. Sci. 20, 729–736 (1965)
Prigogine, I., & P. Glansdoff, Thermodynamic Theory of Structure, Stability and Fluctuations. New York: Wiley-Interscience 1971
Prigogine, I., Structure, Dissipation and Life, in Theoretical Physics and Biology. Amsterdam: North Holland 1969
Donnely, R. I., R. Herman & I. Prigogine, eds., Non-equilibrium Thermodynamics, Variational Techniques and Stability. University of Chicago Press 1965
Prigogine, I., & G. Nicolis, On symmetry-breaking instabilities in dissipative systems. J. Chem. Phys. 46 (6), 3542 (1967)
Prigogine, I., & R. Lefever, Symmetry breaking instabilities in dissipative systems, II. J. Chem. Phys. 48 (4), 1695 (1968)
Lavenda, B., G. Nicolis & M. Herschkowitz-Kaufman, Chemical instabilities and relaxation oscillations. J. Theor. Biol. 32, 283–292 (1971)
Herschkowitz-Kaufman, M., & G. Nicolis, Localized spatial structures and nonlinear chemical waves in dissipative systems. J. Chem. Phys. 56, 1890–1895 (1972)
Zhabotinskii, A. M., Dokl. Acad. Nauk. SSSR, 157, 392 (1964)
Busse, H. B., J. Phys. Chem. 73 (3), 750 (1969)
Chance, B., B. Hess & A. Betz, Biophys. Res. Comm. 16, 182 (1964)
Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton, N. J.: Van Nostrand 1965
Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach, N. Y. 1963
Georgakis, C., M. S. thesis, University of Illinois at Urbana 1972
Iooss, G., Théorie nonlinéaire de la stabilité des écoulements laminaires dans le cas de l'échange de stabilités. Arch. Rational Mech. Anal. 40, 3, 166–208 (1971)
Dunford, N., & J. T. Schwartz, Linear Operators, Vol. I and II. New York: Interscience, N. Y. 1963
Hille, E., & R. S. Phillips, Functional Analysis and Semi-groups. Coll. Publications V. 31, American Math. Society 1957
Krasnoselkii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. New York: Pergamon Press 1964
Steinberg, S., Meromorphic families of compact operators. Arch. Rational Mech. Anal. 31, 5, 372–379 (1968)
Kato, T., Perturbation Theory for Linear Operators. New York: Springer 1963
Kantorovich, L. V., & G. P. Akilov, Functional Analysis in Normed Spaces. International Series of Monograms on Pure and Applied Math., Vol. 64. New York: Pergamon Press 1964
Stakgold, I., Branching of solutions of nonlinear equations. SIAM Review 13 (3), 289–332 (1971)
Stuart, J. T., On the nonlinear mechanics of hydrodynamic stability. J.F.M. 4, 1–21 (1958)
Stuart, J. T., On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows (I). J.F.M. 9, 353–370 (1960)
Watson, J., On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows II. J.F.M. 9, 371–389 (1960)
Eckhaus, W., Studies in Nonlinear Stability Theory. Springer Tracts in Natural Philosophy, Vol. 6. Berlin-Heidelberg-New York: Springer 1965
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Georgakis, C., Sani, R.L. On the stability of the steady state in systems of coupled diffusion and reaction. Arch. Rational Mech. Anal. 52, 266–296 (1973). https://doi.org/10.1007/BF00247738
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DOI: https://doi.org/10.1007/BF00247738