非線性守恆律中擊波解之非守恆積分的不穩定性

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廖鈞妙(Jun-Miao Liao) 查詢紙本館藏

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論文名稱

非線性守恆律中擊波解之非守恆積分的不穩定性
(Instability of Non-Conservative Product to Shock Wave Solutions of Scalar Balance Laws With Singular Source Terms)

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摘要(中)

在這篇論文中，我們考慮單一非線性守恆律的廣義黎曼問題解，
此一守恆律的源項在分佈理論中是奇異的，
代表它是delta函數和非連續函數的乘積。在這篇論文中，
我們將展示一個例子去證明此守恆律中的非守恆乘積是不穩定的。
也就是它的正則型式的積分有不同的值。當解帶有震波時，它們的值取決於震波正則模式的選取。

摘要(英)

In this thesis, we consider the generalized Riemann solutions of scalar nonlinear balance laws
with singular source terms. The source term is singular in the
sense that it is a product of delta function and a discontinuous
function, which is undefined in distribution. We demonstrate an example to show
that the non-conservative product $a′g(u)$ is unstable in the sense that the integral of
regularization $a_{varepsilon}′g(u_{varepsilon})$ for $a′g(u)$ may have multiple values due to the forms $a_varepsilon$, $u_varepsilon$ when $u$ consists of shocks.

關鍵字(中)

★ 非線性守恆律
★ 擊波解
★ 非守恆積分
★ 不穩定性

關鍵字(英)

★ Non-Conservative Product
★ Shock Wave Solutions
★ Singular Source Terms
★ Scalar Balance Laws
★ Instability

論文目次

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Generalized Riemann Solutions and Their Regularization . . . . . . . . 4

3 Instability of Non-conservative Product . . . . . . . . . . . . . . . . . . . 11

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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指導教授

洪盟凱(Meng-Kai Hong)

審核日期

2018-6-21

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