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A perturbation theorem for positive contraction semigroups on L 1-spaces with applications to transport equations and Kolmogorov's differential equations

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Abstract

In this paper, a criterion is given for assuring that a linear positive contraction C 0-semigroup defined on an L 1-space is generated by the closure of A+B, A and B being suitable unbounded linear operators. Furthermore, this criterion is applied to the transport equation, Kolmogorov's differential equations, and a transport equation modelling cell growth.

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References

  1. Arlotti, L.: On the Cauchy problem for the linear Maxwell-Boltzmann equation, J. Differential Equations 69 (1987), 166–184.

    Google Scholar 

  2. Voigt, J.: On substochastic C 0-semigroups and their generators, Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 1984/85.

  3. Hille, E. and Phillips, R. S.: Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ., Providence, R.I., 1957.

    Google Scholar 

  4. Kato, T.: On the semigroups generated by Kolmogoroff's differential equations, J. Math. Soc. Japan 6 (1954), 1–15.

    Google Scholar 

  5. Frosali, G., Van der, Mee, C. V. M., and Paveri-Fontana, S. L.: Conditions for runaway phenomena in the kinetic theory of particle swarms, J. Math. Phys. 30 (1989), 1177–1186.

    Google Scholar 

  6. Kato, T.: Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966.

    Google Scholar 

  7. Molinet, F. A.: Existence, uniqueness and properties of the solutions of the Boltzmann kinetic equation for a weakly ionized gas. I, J. Math. Phys. 18 (1977), 984–996.

    Google Scholar 

  8. Montagnini, B. and Demuru, M. L.: Complete continuity of the free gas scattering operator in neutron thermalization theory, J. Math. Anal. Appl. 12 (1965), 49–57.

    Google Scholar 

  9. Voigt, J.: Functional analytic treatment of the initial boundary value problem for collisionless gases, Habilitationsschrift, Ludwig-Maximilians Universität München, 1981.

  10. Lebowitz, J. L. and Rubinow, S. I.: A theory for the age and generation time distribution of a microbial population, J. Math. Biol. 1 (1974), 17–36.

    Google Scholar 

  11. Greenberg, W., Van der, Mee, C. V. M., and Protopopescu, V.: Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser, Basel, Boston, 1987.

    Google Scholar 

  12. Van der, Mee, C. V. M.: A Transport Equation Modelling Cell Growth, Proceedings of the Workshop Stochastic Modelling in Biology. Relevant Mathematical Concepts and Recent Applications, Heidelberg, August 8–12, 1988, World Scientific, Singapore, to appear.

    Google Scholar 

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  1. Dipartimento di Matematica ‘Vito Volterra’, Università di Ancona, Via Brecce Bianche, I-60313, Ancona, Italy

    Luisa Arlotti

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  1. Luisa Arlotti
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Arlotti, L. A perturbation theorem for positive contraction semigroups on L 1-spaces with applications to transport equations and Kolmogorov's differential equations. Acta Appl Math 23, 129–144 (1991). https://doi.org/10.1007/BF00048802

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  • DOI: https://doi.org/10.1007/BF00048802

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