Boundedness of the solutions of a kind of nonlinear parabolic systems

TL;DR

This paper establishes the boundedness of weak solutions for a class of nonlinear parabolic systems with controlled growth conditions and data in anisotropic Lebesgue spaces.

Contribution

It provides new boundedness results for nonlinear parabolic systems under structural and growth conditions, extending previous theories.

Findings

Weak solutions are essentially bounded.

Results apply to systems with anisotropic Lebesgue space data.

Provides conditions ensuring boundedness of solutions.

Abstract

We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carath\'eodory maps having controlled growth with respect to the solution and the gradient and the data are in anisotropic Lebesgue spaces. Under these assumptions we obtain essential boundedness of the weak solutions.