Author:
Li Yuequn,Liu Hui,Guo Fei
Abstract
We considered a Cauchy problem of a one-dimensional semilinear wave equation with variable-coefficient diffusion, time-dependent damping, and perturbations. The global well-posedness and the asymptotic profile are given by employing scaling variables and the energy method. The lower bound estimate of the lifespan to the solution is obtained as a byproduct.
For more information see https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html
Reference21 articles.
1. Th. Cazenave, A. Haraux, Y. Martel; An Introduction to Semilinear Evolution Equations, Clarendon Press, Oxford, 1998.
2. S. R. Dunbar, H. G. Othmer; On a nonlinear hyperbolic equation describing transmission lines, cell movement, and branching random walks, Nonlinear Oscillations in Biology and Chemistry, Springer-Verlag, Berlin, 66, 1986.
3. H. Fujita; On the blowing up of solutions of the Cauchy problem for ut = ¢u + u1+¿, J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), 109-124.
4. Th. Gallay, G. Raugel; Scaling variables and asymptotic expansions in damped wave equations, J. Differential Equations., 150 (1998), 42-97.
5. L. HNormander,; The Analysis of Linear Partial Differential Operators, III, Springer, Berlin, 2007.