References
N. D. Alikakos,L p bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations4 (1979), 827–868.
J. M. Ball,Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Math. Soc.63 (1977), 370–373.
V. Barbu,Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leiden, 1976.
V. Barbu,Differential perturbations of nonlinear m-accretive operators in Banach spaces, Boll. Un. Mat. Ital.6 (1972), 270–278.
P. Benilan,Operateurs accrétifs et semi-groups dans les espaces L p, Functional Analysis and Numerical Analysis France-Japan Seminar, H. Fujita (ed.), Tokyo, 1978.
P. Benilan and M. G. Crandall,The continuous dependence on ϕ of solutions of u t −Δϕ (u)=0, MRC Technical Summary Report 1942, 1979.
H. Brezis,Opérateurs Maximaux Monotones et Semigroups de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.
H. Brezis and A. Friedman,Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl., to appear.
H. Brezis and W. Strauss,Semi-linear second-order elliptic equations in L 1. J. Math. Soc. Japan25 (1973), 565–590.
M. G. Crandall,An introduction to evolution governed by accretive operators, inDynamical Systems—An Inter. Symp., L. Cesari, J. Hale and J. LaSalle (eds.), Academic Press, New York, 1976, pp. 131–165.
M. G. Crandall and T. Liggett,Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math.93 (1971), 265–298.
M. G. Crandall and A. Pazy,Semigroups of nonlinear contractions and dissipative sets, J. Functional Analysis3 (1969), 376–418.
L. C. Evans,Application of nonlinear semigroup theory to certain partial differential equations, Proc. Symp. Nonlinear Evolution Equations, M. G. Crandall (ed.), Academic Press, New York, 1978, pp. 163–188.
L. C. Evans,Regularity properties for the heat equation subject to nonlinear boundary constraints, Nonlinear Analysis TMA1 (1977), 593–602.
R. H. Martin,Lyapunov functions and autonomous differential equations in a Banach space, Math. Systems Theory7 (1973), 66–72.
A. Pazy,Semigroups of nonlinear contractions and their asymptotic behaviour, inNonlinear Analysis and Mechanics, Heriot-Watt Symp. Vol. III, R. J. Knops (ed.), Pitman Research Notes in Math.30 (1979), 36–134.
L. Véron,Effects regularisants de semi-groupes non linéaires dans les espaces de Banach, Annales Fac. des Sciences Toulouse1 (1979), 171–200.
L. Véron,Coercivité et propriétés régularisantes des semi-groups non linéaires dans les espaces de Banach, to appear.
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Pazy, A. The Lyapunov method for semigroups of nonlinear contractions in Banach spaces. J. Anal. Math. 40, 239–262 (1981). https://doi.org/10.1007/BF02790164
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DOI: https://doi.org/10.1007/BF02790164