This article is cited in 10 papers

Evolution equations with monotone operator and functional non-linearity at the time derivative

G. I. Laptev

Tula State University

Abstract: Conditions for the solubility of the so-called doubly non-linear equations
$$ Au+\frac\partial{\partial t}Bu=f, \qquad u(0)=u_0, $$
are investigated. Here $A$ is a monotone operator induced by a differential expression containing higher-order partial derivatives and $B$ is an operator induced by a monotone function. A theorem on the existence of a solution is proved. The method of monotone operators is used in combination with the method of compact operators. Examples of applications to parabolic differential equations are presented.

UDC: 517.9

MSC: 35K90, 35K65

Received: 13.03.1999

DOI: 10.4213/sm506

 English version: Sbornik: Mathematics, 2000, 191:9, 1301–1322

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