Global regular solutions for the nonhomogeneous Carrier equation

Abstract

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