Almost periodic solutions of anisotropic elliptic-parabolic equations with variable exponents of nonlinearity

Abstract

We prove the well-posedness of Fourier problems for anisotropic elliptic-parabolic equations with variable exponents of nonlinearity without any restrictions at infinity. We obtain estimates of the weak solutions and conditions for the existence of periodic and almost periodic solutions. In addition, some properties of the weak solutions of the Fourier problem are considered.

Keywords

• Fourier problem
• problem without initial conditions
• degenerate implicit equations
• elliptic-parabolic equation
• periodic solution
• almost periodic solution
• nonlinear evolution equation