On a Class of Kirchhoff Type p-Laplacian Evolution Equation with Nonlocal Logarithmic Nonlinearity

We study the Dirichlet problem for a class of Kirchhoff-type evolution equations involving the p-Laplace operator (Formula presented.) where the coefficient of the diffusion and the source terms nonlocally depend on the sought solution. We assume that the coefficient a:[0,∞)→[0,∞) is a non-decreasing function, and a(s)→0 as s→0+; therefore, the equation degenerates as ‖∇u(t)‖p→0. Sufficient conditions for local and global in time solvability of the problem are found. The phenomena of blow-up or vanishing of solutions in a finite time are studied, and the upper bound for the blow-up moment is found.