A reaction-diffusion system arising in modelling man-environment diseases
Authors:
V. Capasso and K. Kunisch
Journal:
Quart. Appl. Math. 46 (1988), 431-450
MSC:
Primary 92A15; Secondary 35K57
DOI:
https://doi.org/10.1090/qam/963580
MathSciNet review:
963580
Full-text PDF Free Access
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Additional Information
- Herbert Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983), no. 2-3, 225–254. MR 719122, DOI https://doi.org/10.1007/BF02774019
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H. Brezis, Operateurs maximaux monotones, North-Holland, Amsterdam, 1973
- V. Capasso and K. Kunisch, A reaction-diffusion system modelling man-environment epidemics, Ann. Differential Equations 1 (1985), no. 1, 1–12. MR 834228
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- Viorel Arnăutu, Viorel Barbu, and Vincenzo Capasso, Controlling the spread of a class of epidemics, Appl. Math. Optim. 20 (1989), no. 3, 297–317. MR 1004711, DOI https://doi.org/10.1007/BF01447658
- K. Kunisch and H. Schelch, Parameter estimation in a special reaction-diffusion system modelling man-environment diseases, J. Math. Biol. 27 (1989), no. 6, 633–665. MR 1024703, DOI https://doi.org/10.1007/BF00276948
H. Schelch, Parameter estimation in a special reaction-diffusion system modelling man-environment diseases specific for the Mediterranean region, Thesis, Technical University of Graz (in German)
H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45, 225–254 (1983)
H. Amann, Nonlinear elliptic equations with nonlinear boundary conditions, New Developments in Differential Equations, W. Eckhaus (Editor), North-Holland Math. Studies 21, 43–63 (1976)
P. Besala, An extension of the strong maximum principle for parabolic equations, Bull. Acad. Polon. Sci. Ser. Math. Astronom. Phys. 11, 1003–1006 (1971)
H. Brezis, Operateurs maximaux monotones, North-Holland, Amsterdam, 1973
V. Capasso and K. Kunisch, A reaction-diffusion system modelling man-environment epidemics, Ann. of Differential Equations 1, 1–12 (1985)
V. Capasso and L. Maddalena, Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases, J. Math. Biol. 13, 173–184 (1981)
V. Capasso and L. Maddalena, On a degenerate nonlinear diffusion problem with boundary feedback, Appl. Analysis 24, 256–298 (1987)
V. Capasso and S. L. Paveri-Fontana, A mathematical model for the 1973 cholera epidemic in the European Mediterranean region, Rev. Epidem. et Santè Publ. 27, 121–132 (1979) (Errata, ibid. 28, 330, 1980)
E. B. Davies, One parameter semigroups, Academic Press, London, 1980
H. O. Fattorini, The Cauchy problem, Encyclopedia of Mathematics and Its Applications, Addison-Wesley, Reading, Mass., 1983
O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural’ceva, Linear and quasilinear equations of parabolic type, Translations Amer. Math. Soc., Providence, 1968
R. M. Martin, Nonlinear operators and differential equations in Banach spaces, John Wiley & Sons, New York, 1976
A. Pazy, Semigroups of linear operators and applications to parabolic differential equations, Springer-Verlag, Berlin, 1983
W. Walter, Differential and integral inequalities, Springer-Verlag, Berlin, 1970
J. Wloka, Partielle Differentialgleichungen, Teubner, Stuttgart, 1982
V. Arnautu, V. Barbu, and V. Capasso, Controlling the spread of a class of epidemics, submitted to Appl. Math. and Optimization
K. Kunisch and H. Schelch, Parameter estimation in a special reaction-diffusion system modelling man-environment diseases, to appear in J. Math. Biology
H. Schelch, Parameter estimation in a special reaction-diffusion system modelling man-environment diseases specific for the Mediterranean region, Thesis, Technical University of Graz (in German)
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Article copyright:
© Copyright 1988
American Mathematical Society