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

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