Existence and attractivity results for a class of degenerate functional-parabolic problems

M. Badii; J. I. Diaz; A. Tesei

Rendiconti del Seminario Matematico della Università di Padova (1987)

  • Volume: 78, page 109-124
  • ISSN: 0041-8994

How to cite

top

Badii, M., Diaz, J. I., and Tesei, A.. "Existence and attractivity results for a class of degenerate functional-parabolic problems." Rendiconti del Seminario Matematico della Università di Padova 78 (1987): 109-124. <http://eudml.org/doc/108072>.

@article{Badii1987,
author = {Badii, M., Diaz, J. I., Tesei, A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {existence; uniqueness; asymptotical behaviour},
language = {eng},
pages = {109-124},
publisher = {Seminario Matematico of the University of Padua},
title = {Existence and attractivity results for a class of degenerate functional-parabolic problems},
url = {http://eudml.org/doc/108072},
volume = {78},
year = {1987},
}

TY - JOUR
AU - Badii, M.
AU - Diaz, J. I.
AU - Tesei, A.
TI - Existence and attractivity results for a class of degenerate functional-parabolic problems
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1987
PB - Seminario Matematico of the University of Padua
VL - 78
SP - 109
EP - 124
LA - eng
KW - existence; uniqueness; asymptotical behaviour
UR - http://eudml.org/doc/108072
ER -

References

top
  1. [1] D.G. Aronson - M.G. Crandall - L.A. Peletier, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. TMA, 6 (1982), pp. 1001-1022. Zbl0518.35050MR678053
  2. [2] P. Baras, Compacité de l'operateur f → u solution d'une equation non linéaire (du/dt) + Au = f, C. R. Acad. Sci. Paris, Sér. A, 286 (1978). pp. 1113-1116. Zbl0389.47030
  3. [3] J. Bebernes - R. ELY, Existence and invariance for parabolic functional equations, Nonlinear Anal. TMA, 7 (1983), pp. 1225-1236. Zbl0544.35084MR721408
  4. [4] H. Brézis, New results concerning monotone operators and nonlinear semigroups, in « Analysis of nonlinear problems », pp. 2-27 (Research Institute for Mathematical Sciences, Kyoto University, 1974). MR493537
  5. [5] H. Brézis - A. FRIEDMAN, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl., 62 (1983), pp. 73-97. Zbl0527.35043MR700049
  6. [6] H. Brézis - W.A. Strauss, Semi-linear second-order elliptic equations in L1, J. Math. Soc. Japan, 25 (1973), pp. 565-590. Zbl0278.35041MR336050
  7. [7] P. DeMOTTONI - A. SCHIAFFINO - A. TESEI, Attractivity properties of nonnegative solutions for a class of nonlinear degenerate parabolic problems, Ann. Mat. Pura Appl., 136 (1984), pp. 35-48. Zbl0556.35083MR765914
  8. [8] J.I. Diaz - J. Hernández, On the existence of a free boundary for a class of reaction-diffusion systems, SIAM J. Math. Anal., 15 (1984), pp. 670-685. Zbl0556.35126MR747428
  9. [9] H. Engler, Invariant sets for functional differential equations in Banach spaces and applications, Nonlinear Anal. TMA, 5 (1981), pp. 1225-1243. Zbl0478.34051MR636733
  10. [10] H. Engler, Functional differential equations in Banach spaces: growth and decay of solutions, J. für Reine u. Angew. Math., 322 (1981), pp. 53-73. Zbl0436.34058MR603026
  11. [11] M.E. Gurtin - R.C. Maccamy, On the diffusion of biological populations, Math. Biosci., 33 (1977), pp. 35-49. Zbl0362.92007MR682594
  12. [12] L.A. Peletier - A. Tesei, Global bifurcation and attractivity of stationary solutions of a degenerate diffusion equation, preprint (1985). Zbl0624.35006
  13. [13] V.P. Politjukov, On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations, Math. USSR Sbornik, 35 (1979), pp. 499-507. Zbl0431.45010MR512008
  14. [14] M.A. Pozio - A. Tesei, Support properties of solutions for a class of degenerate parabolic problems, preprint (1984). Zbl0862.35049MR869102
  15. [15] M.A. Pozio - A. Tesei, Degenerate parabolic problems in population dynamics, Japan J. Appl. Math. (to appear). MR839335
  16. [16] M. Schatzman, Stationary solutions and asymptotic behaviour of a quasilinear degenerate parabolic equation, Indiana Univ. Math. J., 33 (1984), pp. 1-30. Zbl0554.35064MR726104
  17. [17] A. Schiaffino, On a diffusion Volterra equation, Nonlinear Anal. TMA, 3 (1979), pp. 595-600. Zbl0445.45015MR541870
  18. [18] A. Schiaffino - A. Tesei, Asymptotic stability properties for nonlinear diffusion Volterra equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 67 (1979), pp. 227-232. Zbl0463.45008MR622797
  19. [19] A. Schiaffino - A. Tesei, Monotone methods and attractivity results for Volterra integropartial differential equations, Proc. Royal Soc. Edinburgh, 89A (1981), pp. 135-142. Zbl0474.45004MR628134
  20. [20] J. Spruck, Uniqueness in a diffusion model of population biology, Comm. in Partial Differential Equations, 8 (1983), pp. 1605-1620. Zbl0534.35055MR729195
  21. [21] G. Stampacchia, On some regular multiple integral problems in the calculus of variations, Comm. Pure Appl. Math., 16 (1963), pp. 383-421. Zbl0138.36903MR155209
  22. [22] A. Tesei, Stability properties for partial Volterra integrodifferential equations, Ann. Mat. Pura Appl., 126 (1980), pp. 103-115. Zbl0463.45009MR612355
  23. [23] L. Tsai, On integro-differential equations of parabolic type, Bull. Inst. Math. Acad. Sinica, 9 (1981), pp. 311-320. Zbl0465.45011MR625724
  24. [24] V. Volterra, Leçons sur la théorie mathématique de la lutte pour la vie (Paris: Gauthier-Villars, 1931). Zbl0002.04202
  25. [25] I.I. Vrabie, The nonlinear version of Pazy's local existence theorem, Israel J. Math., 32 (1979), pp. 221-235. Zbl0406.34064MR531265
  26. [26] I.I. Vrabie, Compactness methods for an abstract nonlinear Volterra integrodifferential equation, Nonlinear Analysis TMA, 5 (1981), pp . 355-371. Zbl0459.45011MR611648
  27. [27] I.I. Vrabie, An existence result for a class of nonlinear evolution equations in Banach spaces, Nonlinear Analysis TMA, 6 (1982), pp. 711-722. Zbl0493.34050MR664148
  28. [28] Y. Yamada, On a certain class of semilinear Volterra diffusion equations, J. Math. Anal. Appl., 88 (1982), pp. 433-451. Zbl0515.45012MR667070

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.