Initial–boundary value problem of Euler equations with damping in R+n
| Autor: | Linglong Du |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pointwise
Applied Mathematics 010102 general mathematics Boundary (topology) 01 natural sciences Euler equations 010101 applied mathematics Nonlinear system symbols.namesake Fundamental solution symbols Applied mathematics Initial value problem Boundary value problem 0101 mathematics Constant (mathematics) Analysis Mathematics |
| Zdroj: | Nonlinear Analysis. 176:157-177 |
| ISSN: | 0362-546X |
| Popis: | The asymptotic wave behavior of solution for the Euler equations with damping in R + n is investigated around a given constant equilibrium in this paper. Three classical boundary condition cases are considered here. New approaches and techniques are introduced to deal with the multi-dimensional case for the system. For the linearized problem, by comparing symbols in the transformed tangential–spatial and time space, we show that its Green’s function can be described in terms of the fundamental solution for the Cauchy problem and reflected fundamental solution coupled with a boundary operator. Our approaches help us to simplify the Green’s function to the essential part and benefit the follow-up nonlinear analysis. For the nonlinear problem, we prove the pointwise decaying rate with the help of the Duhamel’s principle. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect