A priori estimates of solutions of superlinear problems

Pavol Quittner

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 2, page 483-492
  • ISSN: 0862-7959

Abstract

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In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.

How to cite

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Quittner, Pavol. "A priori estimates of solutions of superlinear problems." Mathematica Bohemica 126.2 (2001): 483-492. <http://eudml.org/doc/248841>.

@article{Quittner2001,
abstract = {In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.},
author = {Quittner, Pavol},
journal = {Mathematica Bohemica},
keywords = {a priori estimate; global existence; parabolic equation; superlinear nonlinearity; blowing-up; global existence; superlinear nonlinearity; blowing-up},
language = {eng},
number = {2},
pages = {483-492},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A priori estimates of solutions of superlinear problems},
url = {http://eudml.org/doc/248841},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Quittner, Pavol
TI - A priori estimates of solutions of superlinear problems
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 483
EP - 492
AB - In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.
LA - eng
KW - a priori estimate; global existence; parabolic equation; superlinear nonlinearity; blowing-up; global existence; superlinear nonlinearity; blowing-up
UR - http://eudml.org/doc/248841
ER -

References

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  1. 10.1080/03605307708820041, Commun. Partial Differ. Equations 2 (1977), 601–614. (1977) MR0509489DOI10.1080/03605307708820041
  2. 10.1080/03605308408820353, Commun. Partial Differ. Equations 9 (1984), 955–978. (1984) MR0755928DOI10.1080/03605308408820353
  3. A priori estimates for positive solutions of semilinear elliptic systems via Hardy-Sobolev inequalities, Nonlinear partial differential equations, A. Benkirane at al (eds.), Pitman Research Notes in Math. 343, Harlow, Longman, 1996, pp. 73–91. (1996) MR1417272
  4. 10.1016/0022-0396(91)90118-S, J. Differ. Equations 89 (1991), 176–202. (1991) MR1088342DOI10.1016/0022-0396(91)90118-S
  5. Linear and nonlinear heat equations in L δ p spaces and universal bounds for global solutions, Preprint. MR1835063
  6. 10.1002/(SICI)1097-0312(199701)50:1<1::AID-CPA1>3.0.CO;2-H, Commun. Pure Applied Math. 50 (1997), 1–67. (1997) MR1423231DOI10.1002/(SICI)1097-0312(199701)50:1<1::AID-CPA1>3.0.CO;2-H
  7. A priori bounds for positive solutions of nonlinear elliptic equations, Commun. Partial Differ. Equations 6 (1991), 883–901. (1991) MR0619749
  8. 10.1007/BF01211756, Commun. Math. Phys. 103 (1986), 415–421. (1986) Zbl0595.35057MR0832917DOI10.1007/BF01211756
  9. 10.1512/iumj.1987.36.36001, Indiana Univ. Math. J. 36 (1987), 1–40. (1987) MR0876989DOI10.1512/iumj.1987.36.36001
  10. 10.1006/jdeq.1996.0143, J. Differ. Equations 130 (1996), 277–291. (1996) MR1410888DOI10.1006/jdeq.1996.0143
  11. Remarks on the blowup estimate for solutions of the heat equation with a nonlinear boundary condition, Differ. Integral Equations 9 (1996), 891–901. (1996) MR1392086
  12. 10.1002/cpa.3160160307, Commun. Pure Appl. Math. 16 (1963), 305–330. (1963) Zbl0156.33503MR0160044DOI10.1002/cpa.3160160307
  13. A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations, Z. Angew. Math. Phys. 42 (1992), 408–430. (1992) MR1115199
  14. 10.1016/0022-0396(84)90145-1, J. Differ. Equations 54 (1984), 97–120. (1984) MR0756548DOI10.1016/0022-0396(84)90145-1
  15. A priori bounds for global solutions of a semilinear parabolic problem, Acta Math. Univ. Comenianae 68 (1999), 195–203. (1999) Zbl0940.35112MR1757788
  16. Universal bound for global positive solutions of a superlinear parabolic problem, Preprint. Zbl0981.35010MR1839765
  17. Signed solutions for a semilinear elliptic problem, Differ. Integral Equations 11 (1998), 551–559. (1998) Zbl1131.35339MR1666269
  18. A priori estimates of global solutions and multiple equilibria of a parabolic problem involving measure, Preprint. 
  19. Transition from decay to blow-up in a parabolic system, Arch. Math. (Brno) 34 (1998), 199–206. (1998) Zbl0911.35062MR1629705
  20. In preparation, . 
  21. Existence of positive solutions of semilinear elliptic systems without variational structure, Preprint. 

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