Semilinear parabolic systems

Herbert Amann

Commentationes Mathematicae Universitatis Carolinae (1985)

  • Volume: 026, Issue: 1, page 3-21
  • ISSN: 0010-2628

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Amann, Herbert. "Semilinear parabolic systems." Commentationes Mathematicae Universitatis Carolinae 026.1 (1985): 3-21. <http://eudml.org/doc/17359>.

@article{Amann1985,
author = {Amann, Herbert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semilinear parabolic systems; local and global existence; time-dependent boundary conditions; regularity},
language = {eng},
number = {1},
pages = {3-21},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Semilinear parabolic systems},
url = {http://eudml.org/doc/17359},
volume = {026},
year = {1985},
}

TY - JOUR
AU - Amann, Herbert
TI - Semilinear parabolic systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1985
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 026
IS - 1
SP - 3
EP - 21
LA - eng
KW - semilinear parabolic systems; local and global existence; time-dependent boundary conditions; regularity
UR - http://eudml.org/doc/17359
ER -

References

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  2. ALIKAKOS N. D., Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems, Proc. Royal Soc. Edinburgh 94 (1983), 265-286. (1983) Zbl0538.35009MR0709721
  3. AMANN H., Existence and regularity for semilinear parabolic evolution equations, To appear. Zbl0625.35045MR0808425
  4. AMANN H., Global existence for semilinear parabolic systems, In preparation. Zbl0564.35060
  5. BROWDER F. E., On the spectral theory of elliptic operastors, I. Math. Annalen 141 (1961), 22-130. (1961) MR0209909
  6. COSNER CH., Pointwise a priori bounds for strongly coupled semi-linear systems of parabolic partial differential equations, Indiana Univ. Math. J. 30 (1981), 607-620. (1981) Zbl0467.35014MR0620270
  7. FRIEDMAN A., Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969. (1969) Zbl0224.35002MR0445088
  8. KATO T., TANABE H., On the abstract evolution equation, Osaka Math. J. 14 (1962), 107-133. (1962) Zbl0106.09302MR0140954
  9. KIELHOEFER H., Global solutions of semi linear evolution equations satisfying an energy inequality, J. Diff. Equat. 36 (1980), 188-222. (1980) MR0574336
  10. LIONS J. L., MAGENES E., Non-Homogeneous Boundary Value Problems and Applications I, Springer Verlag, Berlin, 1972. (1972) 
  11. PECHER H., von WAHL W., Klassische Lösungen in Grossen semilinearer parabolischer Differentialgleichungen, Math. Z. 145 (1975), 255-265. (1975) MR0422872
  12. ROTHE F., Uniform bounds from bounded L p -functionals in reaction-diffusion equations, J. Diff. Equat. 45 (1982), 207-233. (1982) MR0665998
  13. ROTHE F., A priori estimates, global existence and asymptotic behaviour for weakly ooupled systems of reaction-diffusion equations, Habilitationsschrift, Univ. Tübingen, 1983. (1983) 
  14. SOBOLEVSKII P.E., Equations of parabolic type in a Banaoh space, , Amer. Math. Soc. Transl., Ser. 2, 49 (1966), 1-62. (1966) 
  15. von WAHL W., Lineare und semilineare parabolisohe Differentialgleichungen in Räumen hölderstetiger Funktionen, Abh. Math. Sen. Univ. Hamburg 43 (1975), 234-262. (1975) MR0473528
  16. von WAHL W., Semilinear elliptic and parabolic equations of arbitrary order, Proc. Royal Soc. Edinburgh, Sect. A, 78 (1978), 193-207. (1978) Zbl0398.35043MR0492843
  17. YAGI A., On the abstract linear evolution equations in Banach spaces, J. Math. Soc Japan 28 (1976), 290-303. (1976) Zbl0318.34068MR0397478

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