Enclosure statements for systems of semilinear parabolic differential equations Inclusion statements for systems of semilinear parabolic differential equations

Wilhelm Heinrichs

Applications of Mathematics (1991)

  • Volume: 36, Issue: 2, page 96-122
  • ISSN: 0862-7940

Abstract

top
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.

How to cite

top

Heinrichs, Wilhelm. "Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen." Applications of Mathematics 36.2 (1991): 96-122. <http://eudml.org/doc/15663>.

@article{Heinrichs1991,
author = {Heinrichs, Wilhelm},
journal = {Applications of Mathematics},
keywords = {semilinear; asymptotic stability; invariance; biochemical reaction; model for the nerve membrane; asymptotic stability; biochemical reaction; model for the nerve membrane},
language = {ger},
number = {2},
pages = {96-122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen},
url = {http://eudml.org/doc/15663},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Heinrichs, Wilhelm
TI - Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 2
SP - 96
EP - 122
LA - ger
KW - semilinear; asymptotic stability; invariance; biochemical reaction; model for the nerve membrane; asymptotic stability; biochemical reaction; model for the nerve membrane
UR - http://eudml.org/doc/15663
ER -

References

top
  1. E. Abrahams T. Tsuneto, 10.1103/PhysRev.152.416, Phys. Rev. 152 (1968), 416-432. (1968) DOI10.1103/PhysRev.152.416
  2. N. Alikakos, 10.1016/0362-546X(81)90077-8, Nonlinear Analysis 5 (1981), 593-614. (1981) Zbl0463.35044MR0618214DOI10.1016/0362-546X(81)90077-8
  3. H. Amann, 10.1016/0022-247X(78)90192-0, J. Math. Anal. App. 65 (1978), 432-467. (1978) Zbl0387.35038MR0506318DOI10.1016/0022-247X(78)90192-0
  4. N. R. Amundson, Nonlinear problems in chemical reactor theory, SIAM-AMS Proc. 8 (1974), 59-84. (1974) Zbl0314.76066
  5. J. W. Bebernes K. Schmitt, Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations, Rocky Mountain J. Math. 7 (1977), 575-567. (1977) MR0600519
  6. J. A. Boa, 10.1002/sapm19755419, Studies in appl. Math. 54 (1975), 9-15. (1975) Zbl0314.92005MR0452782DOI10.1002/sapm19755419
  7. R. G. Casten C. J. Holland, 10.1137/0133023, SIAM J. Appl. Math. 33 (1977), 353-364. (1977) MR0447760DOI10.1137/0133023
  8. E. Conway D. Hoff J. Smoller, 10.1137/0135001, SIAM J. Appl. Math. 35 (1978), 1-16. (1978) MR0486955DOI10.1137/0135001
  9. R. Courant K. O. Friedrichs, Supersonic flow and shock waves, Interscience Publishers, Inc., New York, 1948. (1948) MR0029615
  10. R. Courant D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc. New York, 1953. (1953) MR0065391
  11. K. N. Chueh C. C. Conley J. A. Smoller, 10.1512/iumj.1977.26.26029, Indiana Univ. Math. J. 26 (1977), 373-392. (1977) MR0430536DOI10.1512/iumj.1977.26.26029
  12. R. Fitzhugh, 10.1016/S0006-3495(61)86902-6, Biophys. J. 1 (1961), 445-466. (1961) DOI10.1016/S0006-3495(61)86902-6
  13. G. R. Gavalas, Nonlinear differential equations of chemically reacting systems, Springer, New York, 1968. (1968) Zbl0174.13401MR0247815
  14. C. Georgakis R. L. San, 10.1007/BF00247738, Arch. Rat. Mech. Anal. 52 (1973), 266-296. (1973) MR0440203DOI10.1007/BF00247738
  15. A. L. Hodgkin A. F. Huxley, 10.1113/jphysiol.1952.sp004764, J. Physiol. 117 (1952), 500-544. (1952) DOI10.1113/jphysiol.1952.sp004764
  16. W. E. Kastenberg, 10.1080/00207177408932612, Internat. J. Control 19 (1974), 73 - 79. (1974) MR0337396DOI10.1080/00207177408932612
  17. R. Lemmert, 10.1007/BF01420575, Math. Ann. 230 (1977), 43-56. (1977) MR0492774DOI10.1007/BF01420575
  18. R. Lemmert, 10.1080/03605307808820066, Comm. Partial Differential Equations 3 (1978), 297-318. (1978) MR0481417DOI10.1080/03605307808820066
  19. R. R. Martin, Jr., 10.1007/BF01344170, Math. Ann. 211 (1974), 155-169. (1974) Zbl0297.35027MR0358449DOI10.1007/BF01344170
  20. J. Nagumo S. Arimoto S. Yoshizawa, Am active pulse transmission line simulating nerve axon, Proc. IRE 50 (1964), 2061 - 2070. (1964) 
  21. J. Rauch J. A. Smoller, 10.1016/0001-8708(78)90075-0, Advances in Math. 27 (1978), 12-44. (1978) MR0487094DOI10.1016/0001-8708(78)90075-0
  22. R. Redheffer W. Walter, 10.1007/BF00280826, Arch. Rat. Mech. Anal. 67 (1978), 41 - 52. (1978) MR0473317DOI10.1007/BF00280826
  23. R. Redheffer W. Walter, Invariant sets for systems of partial differential equations, II. First-order and elliptic equations, Arch. Rat. Mech. Anal. 73 (1980), 19-29. (1980) MR0555580
  24. D. H. Sattinger, 10.1016/0022-247X(68)90025-5, J. Math. Anal. and Appl. 24 (1968), 241-245. (1968) Zbl0192.45002MR0231028DOI10.1016/0022-247X(68)90025-5
  25. C. Schazfer, Invariant sets and contractions for weakly coupled systems of parabolic differential equations, Rendiconti di Mathematica 13 (1980), 337-357. (1980) MR0609478
  26. K. Schmitt, 10.1016/0362-546X(78)90019-6, Nonlinear Anal. 2 (1978), 263-309. (1978) Zbl0378.35022MR0512661DOI10.1016/0362-546X(78)90019-6
  27. J. Schröder, 10.1016/0022-0396(82)90037-7, J. of Diff. Equ. 45 (1982), 431-460. (1982) MR0672717DOI10.1016/0022-0396(82)90037-7
  28. J. Schröder, Operator inequalities, Academic Press, New York, 1980. (1980) MR0578001
  29. H. Triebel, Höhere Analysis, VEB Dsutscher Verlag der Wissenschaften, Berlin, 1972. (1972) Zbl0257.47001MR0360061
  30. V. S. Vladimirov, Equations of mathematical physics, Marcel Dekker, Inc., New York, 1971. (1971) Zbl0231.35002MR0268497
  31. W. Walter, Differential and integral inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete 55. Springer, Berlin, Heidelberg, New York, 1970. (1970) Zbl0252.35005MR0271508
  32. G. N. Watson, A treatise on the theory of Bessel functions, Cambridge at the University Press, 1958. (1958) MR1349110
  33. H. F. Weinberger, Invariants sets for weakly coupled parabolic and elliptic systems, Rendiconti di Mathematica 8, Serie VI (1975), 295-310. (1975) MR0397126

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.