- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 2
- Qualitative analysis of solutions for a Kirchhoff-type parabolic equation with multiple nonlineariti...
Qualitative analysis of solutions for a Kirchhoff-type parabolic equation with multiple nonlinearities
Authors : Erhan Pişkin, Fatma Ekinci
Pages : 397-413
Doi:10.15672/hujms.657295
View : 14 | Download : 5
Publication Date : 2021-04-11
Article Type : Research
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].Keywords : Existence of solutions, Blow up, Exponential growth, Decay, Kirchhoff-type equation