Abstract

We study in an+1-dimensional cylinder Q global solvability of the mixed problem for the nonhomogeneous Carrier equation utt−M(x,t,||u(t)||2)Δu+g(x,t,ut)=f(x,t) without restrictions on a size of initial data and f(x,t). For any natural n, we prove existence, uniqueness and the exponential decay of the energy for global generalized solutions. When n=2, we prove C∞(Q)-regularity of solutions.