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arXiv · 1011.0562

Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators

Wei Liu
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Abstract

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, we show that local monotonicity implies the pseudo-monotonicity. The main result is applied to various types of PDE such as reaction-diffusion equations, generalized Burgers equation, Navier-Stokes equation, 3D Leray-$α$ model and $p$-Laplace equation with non-monotone perturbations.

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Wei Liu. 2010-11-02. Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators. https://doi.org/10.1016/j.na.2011.08.018

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