✦ LIBER ✦

Existence results for a nonlinear evolution equation containing a composition of two monotone operators

✍ Scribed by Nataliya Kraynyukova

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 96 KB
Volume: 34
Category: Article
ISSN: 0936-7195
DOI: 10.1002/gamm.201110011

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We present an existence result for an evolution equation with a nonlinear operator, which is a composition of two monotone mappings. The first monotone mapping is a subdifferential of the indicator function of some convex set while the other is constructed as the Nemyckii operator of a monotone function. Such equations arise from the mathematical models, which describe piezoelectric material behavior. Under some additional assumptions we prove the existence and uniqueness of the strong solution for the case, when the operator generated by the monotone function is a Lipschitz continuous mapping. In the case of a nonlinear growth of the monotone function we prove the existence of the strong solution (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Some Convergence Results for a Class of

Some Convergence Results for a Class of Nonlinear Phase-Field Evolution Equations

✍ Giulio Schimperna 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 203 KB

Two heat diffusion problems in the framework of the parabolic phase-field model are presented. The first problem is related to a single isotropic fluid and the other describes the heat transmission between two different substances in contact. Some known existence and uniqueness results are briefly r