An existence theorem for semilinear functional parabolic equations

Jaroslav Milota; Hana Petzeltová

Časopis pro pěstování matematiky (1985)

  • Volume: 110, Issue: 3, page 274-288
  • ISSN: 0528-2195

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Milota, Jaroslav, and Petzeltová, Hana. "An existence theorem for semilinear functional parabolic equations." Časopis pro pěstování matematiky 110.3 (1985): 274-288. <http://eudml.org/doc/21600>.

@article{Milota1985,
author = {Milota, Jaroslav, Petzeltová, Hana},
journal = {Časopis pro pěstování matematiky},
keywords = {fractional power; local existence; functional differential equation; sectorial operator; Banach space; heat conduction in materials with memory},
language = {eng},
number = {3},
pages = {274-288},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
title = {An existence theorem for semilinear functional parabolic equations},
url = {http://eudml.org/doc/21600},
volume = {110},
year = {1985},
}

TY - JOUR
AU - Milota, Jaroslav
AU - Petzeltová, Hana
TI - An existence theorem for semilinear functional parabolic equations
JO - Časopis pro pěstování matematiky
PY - 1985
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 110
IS - 3
SP - 274
EP - 288
LA - eng
KW - fractional power; local existence; functional differential equation; sectorial operator; Banach space; heat conduction in materials with memory
UR - http://eudml.org/doc/21600
ER -

References

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  1. G. Chen R. Grimmer, Semigroups and integral equations, J. Integгal Equations 2 (1980), 133-154. (1980) MR0572484
  2. G. Chen R. Grimmer, Integral equations as evolution equations, J. Diff. Equations 45 (1982), 53-74. (1982) MR0662486
  3. B. D. Coleman M. E. Gurtin, Equipresence and constitutive equation for rigid hcat conductors, Z. Angew. Math. Phys. 18 (1967), 199-208. (1967) MR0214334
  4. M. G. Crandall S. O. London J. A. Nohel, An abstract nonlinear Volterra integrodifferential equation, J. Мath. Anal. Appl. 64 (1978), 701-735. (1978) MR0500052
  5. K. Darbo, Punti uniti in transformazioni a codominio non compatto, Rend. Sem. Mat. Univ. Padua 24 (1955), 84-92. (1955) MR0070164
  6. N. Dunford J. T. Schwartz, Linear Operators. Part I, Interscience Publ., New York 1958. (1958) MR0117523
  7. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York 1969. (1969) Zbl0224.35002MR0445088
  8. M. E. Gurtin A. C. Pipkin, А general thеory of heat conduction with finite wave speeds, Аrch. Rational Мech. Аnal. 31 (1968), 113-126. (1968) MR1553521
  9. M. L. Heard, Аn abstract semilinear hyperbolic Volterra intеgiodiffеrеntial equation, J. Math. Аnal. Аppl. 80 (1981), 175-202. (1981) MR0614252
  10. M. L. Heard, Аn abstract parabolic Volterra integrodifferential equation, SIАM J. Math. Аnal. 13 (1982), 81-105. (1982) MR0641542
  11. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. No 840. Springer Verlag 1981. (1981) Zbl0456.35001MR0610244
  12. T. Kato, Perturbаtiоn Тheоry fоr Linеаr Opеrаtоrs, Springer Verlаg 1966. (1966) 
  13. J. L. Kelley, Generаl Тоpоlоgy, Vаn Nоstrаnd Cоmp., New Yоrk 1955. (1955) 
  14. K. Kuratowski, Sur les espаces cоmplètes, Fund. Mаth. 15 (1930), 301 -309. (1930) 
  15. R. K Miller, Аn integrоdifferentiаl equаtiоn fоr rigid hеаt cоnductоrs with mеmоry, Ј. Mаth. Аnаl. Аppl. 66 (1978), З1З-ЗЗ2. (1978) 
  16. J. W. Nunziato, On hеаt cоnductiоn in mаtеriаls with mеmоry, Quаrt. Аppl. Mаth. 29 (1971), 187-204. (1971) MR0295683
  17. R. Nussbaum, Тhе fixed pоint index fоr lоcаl cоndensing mаps, Аnn. di Mаt. Purа ed Аppl. 89 (1971), 217-258. (1971) 
  18. A. Pazy, А clаss оf semilineаr equаtiоns оf evоlutiоn, Isrаel Ј. Mаth. 20 (1975), 23 - 36. (1975) 
  19. A. Schiaffino, Cоmpаctness methоd fог а clаss оf semi-lineаr evоlutiоn equаtiоns, Nоnlineаr Аnаlуsis. Тheоrу Methоds & Аppl. 2 (1978), 179-188. (1978) MR0508697
  20. G. Seifert, А temperаture equаtiоn fоr а rigid heаt cоnductоr with memоrу, Quаrt. Аppl. Mаth. 38 (1980), 246-252. (1980) 
  21. C. C. Travis G. F. Webb, Existence, stаbilitу аnd cоmpаctness in the α-nоrm fоr pаrtiаl functiоnаl differentiаl еquаtiоns, Тrаns. Аmer. Mаth. Sоc. 240 (1978), 129- 143. (1978) MR0499583
  22. G. F. Webb, Аn аbstrаct semilineаr Vоlterrа integrоdifferentiаl equаtiоn, Prоc. Аmer. Mаth. Sоc. 69 (1978), 255-260. (1978) 
  23. G. F. Webb, Аbstrаct Vоltеrrа integrоdifferеntiаl еquаtiоns аnd а clаss оf rеаctiоn diffusiоn еquаtiоns, Lеcturе Nоtеs in Mаth. Nо 737, pp. 295-303. Springеr Vеrlаg 1979. (1979) 
  24. K. Schumacher, Rеmаrks оn sеmilinеаr pаrtiаl functiоnаl-diffеrеntiаl еquаtiоns with infinitе dеlау, Ј. Mаth. Аnаl. Аppl. 80 (1981), 261-290. (1981) 

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