Regularizing effects of homogeneous evolution equations. (English) Zbl 0556.35067

Bénilan, Philippe; Crandall, Michael G.

Contributions to analysis and geometry, Suppl. Am. J. Math., 23-39 (1981).

[For the entire collection see Zbl 0538.00002.]
The authors consider homogeneous evolution equations of the form \(u'=B(u)\). They give some abstract results concerning the solutions of the equation and its perturbation. All the results are estimates of the difference quotients \(h^{-1}(u(t+h)-u(t))\) and therefore types of regularizing effects. These abstract results are then used for some particular problems.

Reviewer: J.Schoenenberger-Deuel

MSC:

35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations
35B45	A priori estimates in context of PDEs
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

homogeneous evolution equations; perturbation; estimates; regularizing effects

Citations:

Zbl 0538.00002