Publication:
Parabolic problems with nonlinear boundary conditions and critical nonlinearities

Loading...
Thumbnail Image
Full text at PDC
Publication Date
1999-08-10
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
We prove existence, uniqueness and regularity of solutions For heat equations with nonlinear boundary conditions. We study these problems with initial data in L-q(Omega), W-1,W-q(Omega), 1 < q < infinity or measures and with critically growing non-linearities.
Description
Unesco subjects
Keywords
Citation
R. Adams, "Sobolev Spaces," Academic Press, Boston, 1978. N. D. Alikakos, Regularity and asymptotic behavior for the second order parabolic equation with nonlinear boundary conditions in L p , J. Differential Equations 39 (1981), 311–344. H. Amann, On abstract parabolic fundamental solutions, J. Math. Soc. Japan 39 (1987), 93–116. H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in "Schmeisser/Triebel: Function Spaces, Differential Operators and Nonlinear Analysis," Teubner Texte zur Mathematik, Vol. 133, pp. 9–126, Teubner, Stuttgart, 1993. H. Amann, "Linear and Quasilinear Parabolic Problems. Abstract Linear Theory," Birkhäuser, Basel, 1995. J. Arrieta and A. N. Carvalho, Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations, to appear in Trans. Am. Math. Soc. H. Biagioni and T. Gramchev, On smoothing phenomena for systems of evolution equations with dissipation, preprint. H. Brezis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, in "Contributions to Nonlinear Functional Analysis" (E. Zarantonello, Ed.), pp. 101–165, 1971. H. Brezis, Problèmes unilateraux, J. Math. Pure Appl. 51 (1972), 1–168. H. Brezis and T. Cazenáve, A nonlinear heat equation with singular initial data, J. Anal. Math. 68 (1996), 277–304. H. Brezis and A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl. 62 (1983), 73–97. A. Carvalho, S. M. Oliva, A. L. Pereira, and A. Rodriguez-Bernal, Attractors for parabolic problems with nonlinear boundary conditions, J. Math. Anal. Appl. 207 (1997), 409–461. L. Evans, Regularity properties of the heat equation subject to nonlinear boundary constraints, Nonlinear Anal. 1 (1977), 593–602. D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin, 1981. H. Kozono and M. Yamazaki, Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Comm. Partial Differential Equations 19 (1994), 959–1014. A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhäuser, Basel, 1995. J. Moser, A sharp form of an inequaliy by N. Trudinger, Indiana U. Math. J. 20 (1971), 1077–1092. H. Tribel, "Interpolation Theory, Function Spaces, Differential Operators," North Holland, Amsterdam, 1978. N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473–483. F. B. Weisler, Semilinear evolution equations in Banach spaces, J. Functional Anal. 32 (1979), 277–296. F. B. Weisler, Local existence and nonexistence for semilinear parabolic equations in L p , Indiana U. Math. J. 29 (1980), 79–102.
Collections