An application of Markov operators in differential and integral equations

Jan Malczak

Rendiconti del Seminario Matematico della Università di Padova (1992)

  • Volume: 87, page 281-297
  • ISSN: 0041-8994

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Malczak, Jan. "An application of Markov operators in differential and integral equations." Rendiconti del Seminario Matematico della Università di Padova 87 (1992): 281-297. <http://eudml.org/doc/108254>.

@article{Malczak1992,
author = {Malczak, Jan},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {ergodic theorem; Boltzmann equation; mathematical biology},
language = {eng},
pages = {281-297},
publisher = {Seminario Matematico of the University of Padua},
title = {An application of Markov operators in differential and integral equations},
url = {http://eudml.org/doc/108254},
volume = {87},
year = {1992},
}

TY - JOUR
AU - Malczak, Jan
TI - An application of Markov operators in differential and integral equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1992
PB - Seminario Matematico of the University of Padua
VL - 87
SP - 281
EP - 297
LA - eng
KW - ergodic theorem; Boltzmann equation; mathematical biology
UR - http://eudml.org/doc/108254
ER -

References

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  1. [ArB66] D.G. Aronson - P. Besala, Uniqueness of solutions of the Cauchy problem for parabolic equations, J. Math. Anal. Appl., 13 (1966), pp. 516-526. Zbl0137.29501MR192197
  2. [ArB67a] D.G. Aronson - P. Besala, Uniqueness of positive solutions of parabolic equations with unbounded coefficients, Coll. Math., 18 (1967), pp. 125-135. Zbl0157.17404MR219900
  3. [ArB67b] D.G. Aronson - P. Besala, Parabolic equations with unbounded coefficients, J. Diff. Eqs., 3 (1967), pp. 1-14. Zbl0149.06804MR208160
  4. [Aro65] D.G. Aronson, Uniqueness of positive weak solutions of parabolic equations, Ann. Polon. Math., 16 (1965), pp. 285-303. Zbl0137.29403MR176231
  5. [Bes75] P. Besala, On the existence of a fundamental solution for parabolic differential equation with unbounded coefficients, Ann. Polon. Math., 29 (1975), pp. 403-409. Zbl0305.35047MR422862
  6. [Bod66] W. Bodanko, Sur le probléme de Cauchy et les problémes de Fourier pour les équations paraboliques dans un domaine non borné, Ann. Polon. Math., 18 (1966), pp. 79-74. Zbl0139.05504MR197998
  7. [Cha70a] J. Chabrowski, Remarques sur l'unicité du probléme de Cauchy, Colloq. Math., 21 (1970), pp. 133-139. Zbl0193.38802MR257554
  8. [Cha70b] J. Chabrowski, Sur la construction de la solution fondamentale de l'équation parabolique aux coefficients non borné, Colloq. Math., 21 (1970), pp. 141-148. Zbl0193.38803MR261164
  9. [Eid69] S.D. Eidelman, Parabolic Systems, North-Holland Publ. Company, Amsterdam and Wolters-Noordhoff Publ., Gröningen (1969). Zbl0181.37403MR252806
  10. [Fel65] J. Feldman, Integral kernels and invariant measures for Markov transition functions, Ann. Math. Statist., 36 (1965), pp. 517-523. Zbl0203.17901MR175178
  11. [Fog69] S.R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold, New York (1969). Zbl0282.60037MR261686
  12. [Fri64] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964). Zbl0144.34903MR181836
  13. [IK062] A.M. Il'in - A.S. Kalashnikov - O.A. Olejnik, Second order linear equations of parabolic type, Russian Math. Surveys (Uspiehi Mat. Nauk.), 17, 3 (1962), pp. 1-143. MR138888
  14. [Krz64] M. Krzy, Sur les solutions non negative de l'équation lineaire normale parabolique, Rev. Roum. Math. Pures Appl., 9 (1964), pp. 393-408. Zbl0168.35903MR182813
  15. [LaM85] A. Lasota - M.C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press (1985). Zbl0606.58002MR832868
  16. [Ser54] J. Serrin, A uniqueness theorem for the parabolic equation ut = = a(x) uxx + b(x) ux + c(x) u, Bull. Amer. Math. Soc., 60 (1954), p. 344. 
  17. [TyH86] J.J. Tyson - K.B. Hannsgen, Cell growth and division: a deterministic/probabilistic model of the cell cycle, J. Math. Biology, 23 (1986), pp. 231-246. Zbl0582.92020MR829135
  18. [Wid44] D. Widder, Positive temperatures on an infinite rod, Trans. Amer. Math. Soc., 55 (1944), pp. 85-95. Zbl0061.22303MR9795

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