Global regular solutions for the nonhomogeneous carrier equation (Q1876958)

Summary: We study in an \(n+1\)-dimensional cylinder \(Q\) global solvability of the mixed problem for the nonhomogeneous Carrier equation \[ u_{tt}- M\biggl(x,t, \bigl\| u(t)\bigr\|^2\biggr) \Delta u+g(x,t, u_t) =f(x,t) \] 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 \(C^\infty(Q)\)-regularity of solutions.