Characterization of the generators of C 0 semigroups which leave a convex set invariant

H. N. Bojadziev

Commentationes Mathematicae Universitatis Carolinae (1984)

  • Volume: 025, Issue: 1, page 159-170
  • ISSN: 0010-2628

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Bojadziev, H. N.. "Characterization of the generators of $C_0$ semigroups which leave a convex set invariant." Commentationes Mathematicae Universitatis Carolinae 025.1 (1984): 159-170. <http://eudml.org/doc/17306>.

@article{Bojadziev1984,
author = {Bojadziev, H. N.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = { semigroup; invariant set; semigroup of operators; closed convex subset with nonempty interior; generalized maximum principle; boundary conditions; support function; generators of positive semigroups},
language = {eng},
number = {1},
pages = {159-170},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterization of the generators of $C_0$ semigroups which leave a convex set invariant},
url = {http://eudml.org/doc/17306},
volume = {025},
year = {1984},
}

TY - JOUR
AU - Bojadziev, H. N.
TI - Characterization of the generators of $C_0$ semigroups which leave a convex set invariant
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1984
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 025
IS - 1
SP - 159
EP - 170
LA - eng
KW - semigroup; invariant set; semigroup of operators; closed convex subset with nonempty interior; generalized maximum principle; boundary conditions; support function; generators of positive semigroups
UR - http://eudml.org/doc/17306
ER -

References

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  1. W. ARENDT P. R. CHERNOFF T. KATO, A generalization of dissipativity and positive semigroups, J. Operator Theory, 8 (1982), 167-180. (1982) MR0670183
  2. V. BARBU, Nonlinear semigroups and differential equations in Banach spaces, Bucuresti/Leyden, 1976. (1976) Zbl0328.47035MR0390843
  3. HR. N. BOJADZIEV, Unbounded generators of positive semigroups on B * -algebras, C. R. Acad. Bulgare Sci., 35 (1982), N. 8, 1033-1036. (1982) Zbl0513.47026MR0687397
  4. O. BRATTELI D. W. ROBINSON, Positive C 0 semigroups on C * -algebras, Math. Scand., 49 (1981), 259-274. (1981) MR0661895
  5. O. BRATTELI T. DIGERNES D. W. ROBINSON, Positive semigroups on ordered Banach spaces, J. Operator Theory, 9 (1983), 371-400. (1983) MR0703815
  6. N. DUNFORD J. T. SCHWARTZ, Linear Operators, Part I, N. Y., 1958. (1958) 
  7. E. B. DYNKIN, Markovskie processi, Moskva, 1963. (In Russian, English translation 1965.) (1963) 
  8. D. E. EVANS H. HANCHE-OLSEN, The generators of positive semigroups, J. Func. Anal., 32 (1979), 207-212. (1979) MR0534674
  9. W. FELLER, The general diffusion operator and positivity preserving semigroups in one dimension, Ann. of Math., 60 (1954), 417-436. (1954) Zbl0057.09805MR0065809
  10. N. HASEGAWA, On contraction semi-groups and (di)-operators, J. Math. Soc. Japan, 18 (1966), 209-302. (1966) Zbl0149.10301MR0201984
  11. G. JAMESON, Ordered linear spaces, Lecture Notes in Math., 141, Berlin, 1970. (1970) Zbl0196.13401MR0438077
  12. R. H. MARTIN, Jr., Nonlinear operators and differential equations in Banach spaces, N. Y., 1976. (1976) Zbl0333.47023
  13. R. S. PHILLIPS, Semigroups of positive contraction operators, Czechoslovak Math. 3., 12 (1962), 294-313. (1962) MR0146675
  14. JEAN-PIERE ROTH, Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues, Ann. Inst. Fourier (Grenoble), 26 (1976), N.4, 1-97. (1976) MR0448158
  15. K. SATO, On the generators of non-negative contraction semigroups in Banach lattices, J. Math. Soc. Japan, 20 (1968), 423-436. (1968) MR0231243
  16. K. DEIMLING, Ordinary differential equations in Banach spaces, Lecture Notes in Math. 596, Berlin, 1977. (1977) Zbl0361.34050MR0463601
  17. R. H. MARTIN., Jr., Invariant sets for evolution systems, International Conf. Diff. Equations (H. Antosiewicz, Ed.), N. Y., London, 1976. (1976) 
  18. R. H. MARTIN, Jr., Invariant sets and a mathematical model involving semilinear differential equations, Nonlinear Equations in Abstract Spaces. N. Y., London, 1978. (1978) Zbl0453.34050
  19. M. NAGUMO, Uber die Lage der Integralkurven gewöhnlicher Differentiallaichungen, Proc. Phys. Math. Soc. Japan, 24 (1942), 551-559. (1942) MR0015180
  20. R. M. REDHEFFER W. WALTER, Flow-invariant sets and differential inequalities in normed spaces, Applicable Anal., 5 (1975), 149-161. (1975) MR0470401
  21. A. D. VENTZEL, On the boundary condition for multidimensional diffusion processes, Teor. verojatnostei i primenenija, 4 (1959), 172-185 (in Russian). (1959) 
  22. P. VOLKMANN, Über die Invarianz konvexer Mengen und Differentialgleichunge in einem normierten Raume, Math. Ann., 203 (1973), 201-210. (1973) MR0322305
  23. P. VOLKMANN, Über die Invarianzsätze von Bony und Brazis in normierten Räumen, Archiv Math., 26 (1975), 89-93. (1975) MR0454238

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