Evolution generated by semilinear dissipative plus compact operators

Schechter, Eric

doi:10.1090/S0002-9947-1983-0678351-X

Evolution generated by semilinear dissipative plus compact operators
HTML articles powered by AMS MathViewer

by Eric Schechter PDF

Trans. Amer. Math. Soc. 275 (1983), 297-308 Request permission

Abstract:

Existence results and sharp continuous dependence results are given for an evolution equation in an arbitrary Banach space. The right-hand side of the equation consists of a linear dissipative term plus a continuous dissipative term plus a compact term.

References

Zvi Artstein, Continuous dependence of solutions of operator equations. I, Trans. Amer. Math. Soc. 231 (1977), no. 1, 143–166. MR 445351, DOI 10.1090/S0002-9947-1977-0445351-1
V. Barbu, Continuous perturbations of nonlinear $m$-accretive operators in Banach spaces, Boll. Un. Mat. Ital. (4) 6 (1972), 270–278 (English, with Italian summary). MR 0326514

Nonlinear semigroups and differential equations in Banach spaces

Aldo Belleni-Morante, Applied semigroups and evolution equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 548865

Equations d’évolution dans un espace de Banach quelconque et applications

Michael G. Crandall and L. C. Evans, On the relation of the operator $\partial /\partial s+\partial /\partial \tau$ to evolution governed by accretive operators, Israel J. Math. 21 (1975), no. 4, 261–278. MR 390853, DOI 10.1007/BF02757989
M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265–298. MR 287357, DOI 10.2307/2373376
M. G. Crandall and A. Pazy, An approximation of integrable functions by step functions with an application, Proc. Amer. Math. Soc. 76 (1979), no. 1, 74–80. MR 534393, DOI 10.1090/S0002-9939-1979-0534393-0

Linear operators

Lawrence C. Evans, Application of nonlinear semigroup theory to certain partial differential equations, Nonlinear evolution equations (Proc. Sympos., Univ. Wisconsin, Madison, Wis., 1977) Publ. Math. Res. Center Univ. Wisconsin, vol. 40, Academic Press, New York-London, 1978, pp. 163–188. MR 513818

Semigroups of operators and applications

Robert H. Martin Jr., Nonlinear operators and differential equations in Banach spaces, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1976. MR 0492671
Michel Pierre, Perturbations localement Lipschitziennes et continues d’opérateurs $m$-accrétifs, Proc. Amer. Math. Soc. 58 (1976), 124–128 (French, with English summary). MR 417863, DOI 10.1090/S0002-9939-1976-0417863-2
Eric Schechter, One-sided continuous dependence of maximal solutions, J. Differential Equations 39 (1981), no. 3, 413–425. MR 612595, DOI 10.1016/0022-0396(81)90066-8
Eric Schechter, Existence and limits of Carathéodory-Martin evolutions, Nonlinear Anal. 5 (1981), no. 8, 897–930. MR 628110, DOI 10.1016/0362-546X(81)90093-6
Eric Schechter, Evolution generated by continuous dissipative plus compact operators, Bull. London Math. Soc. 13 (1981), no. 4, 303–308. MR 620042, DOI 10.1112/blms/13.4.303
Eric Schechter, Interpolation of nonlinear partial differential operators and generation of differentiable evolutions, J. Differential Equations 46 (1982), no. 1, 78–102. MR 677585, DOI 10.1016/0022-0396(82)90111-5
Peter Volkmann, Ein Existenzsatz für gewöhnliche Differentialgleichungen in Banachräumen, Proc. Amer. Math. Soc. 80 (1980), no. 2, 297–300 (German, with English summary). MR 577763, DOI 10.1090/S0002-9939-1980-0577763-5
Zdenek Vorel, Continuous dependence on parameters, Nonlinear Anal. 5 (1981), no. 4, 373–380. MR 611649, DOI 10.1016/0362-546X(81)90021-3