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Publication
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| Title of Article |
On the generalized solutions of the fifth-order Euler equations |
| Date of Acceptance |
1 May 2018 |
| Journal |
| Title of Journal |
Far East Journal of Mathematical Sciences (FJMS) |
| Standard |
OTHER () |
| Institute of Journal |
Pushpa publishing house |
| ISBN/ISSN |
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| Volume |
2018 |
| Issue |
106 |
| Month |
กันยายน |
| Year of Publication |
2018 |
| Page |
59-74 |
| Abstract |
In this paper, we propose the generalized solutions of the fifth-order Euler equations of the form
\begin{align*}
t^5y^{(5)}(t)+a_4t^4y^{(4)}(t)+a_3t^3y'''(t)+a_2t^2y''(t)+a_1ty'(t)+a_0y(t)=0,
\end{align*}
where $a_0, a_1, \ldots, a_4$ are real constants and $t\in\mathbb{R}$. Using Laplace transform technique, we find that the types of Laplace transformable solutions in the space of right-sided distributions depend on the relationship of the values of $a_0, a_1, \ldots, a_4$. To be precise, we have a distributional solution if $k^5+10k^4+35k^3+50k^2+24k=(k^4+6k^3+11k^2+6k)a_4-(k^3+3k^2+2k)a_3+(k^2+k)a_2-ka_1-a_0$ for $k \in \mathbb{N}$, and a weak solution if $ k^5-10k^4+35k^3-50k^2+24k=(-k^4+6k^3-11k^2+6k)a_4+(-k^3+3k^2-2k)a_3+(-k^2+k)a_2-ka_1-a_0$ for $k \in \mathbb{N}\cup\{0\}$. |
| Keyword |
generalized solutions, distributional solutions, weak solutions, Dirac delta function, Euler equation, Laplace transform. |
| Author |
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| Reviewing Status |
ไม่มีผู้ประเมินอิสระ |
| Status |
ตีพิมพ์แล้ว |
| Level of Publication |
นานาชาติ |
| citation |
false |
| Part of thesis |
true |
| Attach file |
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| Citation |
0
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Journal Publication
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