Qualitative analysis of solutions for a Kirchhoff-type parabolic equation with multiple nonlinearities

Abstract

In this work, the local and global existence of weak solutions by using the Faedo-Galerkin method, the finite time blow up of the weak solution with positive initial energy and the general decay of the solution are discussed. Finally, we consider the exponential growth of the solution with sufficient conditions. This work generalizes and improves earlier results in the literature, see [L.X. Truong and N. Van Y, On a class of nonlinear heat equations with viscoelastic term, Comput. Math. Appl., 2016] and [L.X. Truong and N. Van Y, Exponential growth with ${L}^{p}$-norm of solutions for nonlinear heat equations with viscoelastic term, Appl. Math. Comput., 2016].