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Asymptotic profile of solutions for the damped wave equation with a nonlinear convection term
- Source :
- Mathematical Methods in the Applied Sciences. 40:7760-7779
- Publication Year :
- 2017
- Publisher :
- Wiley, 2017.
-
Abstract
- This paper is concerned with the large time behavior of solutions to the initial value problem for the damped wave equations with nonlinear convection in one-dimensional whole space. In 2007, Ueda and Kawashima showed that the solution tends to a self similar solution of the Burgers equation. However, they did not mention that their decay estimate is optimal or not. Under this situation, the aim of this paper was to find out the sharp decay estimate by studying the second asymptotic profile of solutions. The explicit representation formula and the decay estimates of the solution for the linearized equation including the lower order term play crucial roles in our analysis.
- Subjects :
- General Mathematics
010102 general mathematics
Mathematical analysis
General Engineering
Lower order
Damped wave
Space (mathematics)
01 natural sciences
Burgers' equation
Term (time)
010101 applied mathematics
Initial value problem
Nonlinear convection
0101 mathematics
Representation (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........66f3d89b6b8c5058b1d48a115ac9667b