References
Amann, H.: Dual semigroups and second order linear elliptic boundary value problems. Isr. J. Math.45, 225–254 (1983)
Deimling, K.: Nichtlineare Gleichungen und Abbildungsgrade. Berlin Heidelberg New York: Springer 1974
Dafermos, C.M.: Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity. Siam J. Math. Anal.13, 397–408 (1982)
Ebel, W.: Lösungen bei Reaktions-Diffusions-Modellen für den trägervermittelten erleichterten Transport durch biologische Membranen. Dissertation, Tübingen 1983
Ebel, W.: Stationary solutions in a model for carrier facilitated diffusion through a membrane. J. Differ. Equations60, 218–235 (1985)
Friedman, A.: Partial differential equations. New York Chicago San Francisco: Holt, Rinehart and Winston, Inc. 1969
Hadeler, K.P., Rothe, F., Vogt, H.: Stationary solutions of reaction-diffusion equations. Math. Methods Appl. Sci.1, 418–431 (1979)
Henry, D.: Geometric theory of semilinear parabolic equations. Springer Lecture Notes bd840. Berlin Heidelberg New York: Springer 1981
Larsson, S.: On reaction-diffusion equations and their approximation by finite element methods. Dissertation, Göteborg 1985
Mochizuki, M., Forster, R.E.: Diffusion of carbon monoxide through thin layers of hemoglobin solutions. Science138, 897–898 (1962)
Nedelman, J., Rubinow, S.I.: Facilitated diffusion of oxygen and carbon monoxide in the large affinity regime. J. Math. Biol.12, 73–90 (1981)
Ovchinnikov, Y.A.: Physico-chemical, basis of ion transport through biological membranes: Ionophores and ion channels. Eur. J. Biochem.94, 321–336 (1979)
Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. 2: Fourier analysis, selfadjointness. New York: Academic Press 1975
Rothe, F.: Solutions for systems of nonlinear elliptic equations with nonlinear boundary conditions. Math. Methods Appl. Sci.1, 545–553 (1979)
Rothe, F.: Uniform bounds from boundedL p-functionals in reaction-diffusion equations. J. Differ. Equations45, 207–233 (1982)
Rothe, F.: Global solutions of reaction-diffusion systems. Springer Lecture Note1072. Berlin Heidelberg New York Tokyo Springer 1984
Scholander, P.F.: Oxygen transport through hemoglobin solutions. Science131, 585–590 (1960)
Stewart, H.B.: Generation of analytic semigroups by strongly elliptic operators under general boundary conditions. Trans. Am. Math. Soc.259, 299–310 (1980)
Widdas, W.F.: Facilitated transfer of hexoses across the human erythrocyte membrane. J. Physiol.125, 163 (1954)
Wittenberg, J.B.: The molecular mechanism of hemoglobin-facilitated oxygen diffusion. J. Biol. Chem.241, 104–114 (1966)
Wittenberg, J.B.: Myoglobin-facilitated oxygen diffusion: Role of myoglobin in oxygen entry into muscle. Physiol. Rev.50, S. 559 (1970)
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Ebel, W. Existence and asymptotic behaviour of solutions in a system of reaction diffusion equations. Math Z 193, 41–66 (1986). https://doi.org/10.1007/BF01163353
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DOI: https://doi.org/10.1007/BF01163353