# zbMATH — the first resource for mathematics

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.

##### 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