Boundedness of the solutions of a kind of nonlinear parabolic systems

Abstract

We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carathéodory 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.

16 pages

References in corpus (4)

• Boundedness of the solutions to nonlinear systems with Morrey data
• Boundedness of Solutions to a Class of Coercive Systems with Morrey Data
• Asymptotically regular operators in generalized Morrey spaces
• Precise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data

Cited by in corpus (1)

• Quasilinear Cauchy-Dirichlet problem for parabolic equations with $VM{O}_x$ coefficients