Special Session 28: Qualitative theory of nonlinear elliptic and parabolic equations

Boundedness of the solutions of a kind of nonlinear parabolic systems

Lyoubomira Softova
University of salerno
Italy
Co-Author(s):    Emilia Anna Alfano, Luisa Fattorusso
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.