Local existence and uniqueness of weak solutions for nonlinear parabolic equations with superlinear growth and unbounded initial data

Advances in Differential Equations

Volumn 6, Issue 1, 2001, Pages 73-128

  Porretta, Alessio ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

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[No Author keywords available]

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EID: 33748767621     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. D. Andreucci, Degenerate parabolic equations with initial data measures, Trans. Amer. Math. Soc., 349 (1997), 3911-3923.
2. P. Baras and L. Cohen, Complete blow-up after Tmax for the solution of a semilinear heat equation, J. Functional Anal., 71 (1987), 142-174.
3. L. Boccardo and T. Gallouët, Nonlinear elliptic and parabolic equations with measure data, J. Funct. Anal., 87 (1989), 149-169.
4. H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, Journal d'Anal. Math., 68 (1996), 277-304.
5. E. DiBenedetto, "Nonlinear Degenerate Parabolic Equations," Springer-Verlag, 1992.
6. Y. Giga, Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system, J. Diff. Equat., 62 (1986), 186-212.
7. J.L. Lions, "Quelques méthodes de résolution des problemes aux limites non lineaires," Dunod et Gauthiers-Villars, 1969.
8. O.A. Ladyzhenskaja, V. Solonnikov, and N.N. Uraltceva, "Linear and Quasilinear Parabolic Equations," Academic Press, 1970.
9. W.M. Ni and P. Sacks, Singular behavior in nonlinear parabolic equations, Trans. Amer. Math. Soc., 287 (1985), 657-671.
10. F.B. Weissler, Semilinear evolution equations in Banach spaces, J. Funct. Analysis, 32 (1979), 277-296.
11. F.B. Weissler, Local existence and nonexistence for semilinear parabolic equations in Lp, Indiana Univ. Math. J., 29 (1980), 79-102.79