| Title:
|
An existence theorem for semilinear functional parabolic equations (English) |
| Author:
|
Milota, Jaroslav |
| Author:
|
Petzeltová, Hana |
| Language:
|
English |
| Journal:
|
Časopis pro pěstování matematiky |
| ISSN:
|
0528-2195 |
| Volume:
|
110 |
| Issue:
|
3 |
| Year:
|
1985 |
| Pages:
|
274-288 |
| . |
| Category:
|
math |
| . |
| MSC:
|
45N05 |
| idZBL:
|
Zbl 0592.45012 |
| idMR:
|
MR808078 |
| DOI:
|
10.21136/CPM.1985.118234 |
| . |
| Date available:
|
2009-09-23T09:32:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118234 |
| . |
| Reference:
|
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| Reference:
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[2] G. Chen R. Grimmer: Integral equations as evolution equations.J. Diff. Equations 45 (1982), 53-74. MR 0662486 |
| Reference:
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[З] B. D. Coleman M. E. Gurtin: Equipresence and constitutive equation for rigid hcat conductors.Z. Angew. Math. Phys. 18 (1967), 199-208. MR 0214334 |
| Reference:
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[4] M. G. Crandall S. O. London J. A. Nohel: An abstract nonlinear Volterra integrodifferential equation.J. Мath. Anal. Appl. 64 (1978), 701-735. MR 0500052 |
| Reference:
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[5] K. Darbo: Punti uniti in transformazioni a codominio non compatto.Rend. Sem. Mat. Univ. Padua 24 (1955), 84-92. MR 0070164 |
| Reference:
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[6] N. Dunford J. T. Schwartz: Linear Operators. Part I.Interscience Publ., New York 1958. MR 0117523 |
| Reference:
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[7] A. Friedman: Partial Differential Equations.Holt, Rinehart and Winston, New York 1969. Zbl 0224.35002, MR 0445088 |
| Reference:
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[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. MR 1553521 |
| Reference:
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[9] M. L. Heard: Аn abstract semilinear hyperbolic Volterra intеgiodiffеrеntial equation.J. Math. Аnal. Аppl. 80 (1981), 175-202. MR 0614252 |
| Reference:
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[10] M. L. Heard: Аn abstract parabolic Volterra integrodifferential equation.SIАM J. Math. Аnal. 13 (1982), 81-105. MR 0641542 |
| Reference:
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[11] D. Henry: Geometric Theory of Semilinear Parabolic Equations.Lecture Notes in Math. No 840. Springer Verlag 1981. Zbl 0456.35001, MR 0610244 |
| Reference:
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[12] T. Kato: Perturbаtiоn Тheоry fоr Linеаr Opеrаtоrs.Springer Verlаg 1966. |
| Reference:
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[13] J. L. Kelley: Generаl Тоpоlоgy.Vаn Nоstrаnd Cоmp., New Yоrk 1955. |
| Reference:
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[14] K. Kuratowski: Sur les espаces cоmplètes.Fund. Mаth. 15 (1930), 301 -309. |
| Reference:
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[15] R. K Miller: Аn integrоdifferentiаl equаtiоn fоr rigid hеаt cоnductоrs with mеmоry.Ј. Mаth. Аnаl. Аppl. 66 (1978), З1З-ЗЗ2. |
| Reference:
|
[16] J. W. Nunziato: On hеаt cоnductiоn in mаtеriаls with mеmоry.Quаrt. Аppl. Mаth. 29 (1971), 187-204. MR 0295683 |
| Reference:
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[17] R. Nussbaum: Тhе fixed pоint index fоr lоcаl cоndensing mаps.Аnn. di Mаt. Purа ed Аppl. 89 (1971), 217-258. |
| Reference:
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[18] A. Pazy: А clаss оf semilineаr equаtiоns оf evоlutiоn.Isrаel Ј. Mаth. 20 (1975), 23 - 36. |
| Reference:
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[19] A. Schiaffino: Cоmpаctness methоd fог а clаss оf semi-lineаr evоlutiоn equаtiоns.Nоnlineаr Аnаlуsis. Тheоrу Methоds & Аppl. 2 (1978), 179-188. MR 0508697 |
| Reference:
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[20] G. Seifert: А temperаture equаtiоn fоr а rigid heаt cоnductоr with memоrу.Quаrt. Аppl. Mаth. 38 (1980), 246-252. |
| Reference:
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[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. MR 0499583 |
| Reference:
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[22] G. F. Webb: Аn аbstrаct semilineаr Vоlterrа integrоdifferentiаl equаtiоn.Prоc. Аmer. Mаth. Sоc. 69 (1978), 255-260. |
| Reference:
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[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. |
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[24] K. Schumacher: Rеmаrks оn sеmilinеаr pаrtiаl functiоnаl-diffеrеntiаl еquаtiоns with infinitе dеlау.Ј. Mаth. Аnаl. Аppl. 80 (1981), 261-290. |
| . |
