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Semi-linear evolution equations in interpolation spaces. (English) Zbl 0357.34061


MSC:

34G99 Differential equations in abstract spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35K55 Nonlinear parabolic equations
45N05 Abstract integral equations, integral equations in abstract spaces
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References:

[1] Sobolevski, P. E., Equations of Parabolic Type in a Banach Space, Trudy Mosk. mat. Obshch., 10, 297-350 (1961)
[2] Friedman, A., Remarks on Nonlinear Parabolic Equations, (Proc. Symp. appl. Math., 17 (1965)), 5-23
[3] Maruo, K., Integral Equation Associated with Some Non-Linear Evolution Equation, J. math. Soc. Japan, 26, 433-439 (1974) · Zbl 0281.45017
[4] Webb G.F.; Webb G.F.
[5] Lions, J. L.; Peetre, J., Sur une Classe d’Espaces d’Interpolation Publications Mathématiques de l’I.S.H.E., 19, 5-68 (1964) · Zbl 0148.11403
[6] Grisvard, P., Spazi di Tracce ed Applicazioni, Rend. Mat., 5, 4, 657-729 (1972) · Zbl 0272.46025
[7] Da Prato, G.; Grisvard, P., Sommes d’Opérateurs Linéaires et Equations Différentielles Operationnelles, J. Math. pures appl., 54, 305-387 (1975) · Zbl 0315.47009
[8] Grisvard, P., Commutativitè de deux Foncteurs d’Interpolation et Applications, J. Math. pures appl., 45, 143-290 (1966) · Zbl 0173.15803
[9] Kato, T., Nonlinear Semigroups and Evolution Equations, J. math. Soc. Japan, 19, 508-519 (1967) · Zbl 0163.38303
[10] Da Prato, G., Applications Croissantes et Equations d’Evolution dans les Espaces de Banach, Ist. Naz. Alta. Mat. Roma (1975), Academic Press (to appear) · Zbl 0352.47002
[11] Friedman, A., Partial Differential Equations (1969), Holt, Rinehart and Winston: Holt, Rinehart and Winston New York
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