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pro vyhledávání: '"Duong, Giao Ky"'
We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schr\"odinger operator $-\Delta - (d-2)^2/(4|x|^2) -W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted $L^{d/2}-$norm of $W$ whi
Externí odkaz:
http://arxiv.org/abs/2312.16482
In this paper, we consider the complex Ginzburg-Landau equation $$ \partial_t u = (1 + i \beta) \Delta u + (1 + i \delta) |u|^{p-1}u - \alpha u, \quad \text{where } \beta, \delta, \alpha \in \mathbb{R}. $$ The study focuses on investigating the finit
Externí odkaz:
http://arxiv.org/abs/2308.02297
In this paper, we revisit the proof of the existence of a solution to the semilinear heat equation in one space dimension with a at blowup profile, already proved by Bricmont and Kupainen together with Herrero and Vel\'{a}zquez. Though our approach r
Externí odkaz:
http://arxiv.org/abs/2206.04378
Publikováno v:
In Journal de mathématiques pures et appliquées October 2024 190
Akademický článek
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We construct a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile.
Comment: 85 pages. arXiv admin note: s
Comment: 85 pages. arXiv admin note: s
Externí odkaz:
http://arxiv.org/abs/1912.05922
Autor:
Duong, Giao Ky, Zaag, Hatem
In this paper, we are interested in the mathematical model of MEMS devices which is presented by the following equation on $(0,T) \times \Omega:$ \begin{eqnarray*} \partial_t u = \Delta u +\displaystyle \frac{\lambda }{ (1-u)^2 \left( 1 +\displaystyl
Externí odkaz:
http://arxiv.org/abs/1811.11483
Autor:
Duong, Giao Ky
In this paper, we consider the following semi-linear complex heat equation \begin{eqnarray*} \partial_t u = \Delta u + u^p, u \in \mathbb{C} \end{eqnarray*} in $\mathbb{R}^n,$ with an arbitrary power $p,$ $ p > 1$. In particular, $p$ can be non integ
Externí odkaz:
http://arxiv.org/abs/1804.00560
Autor:
Duong, Giao Ky
In this paper, we consider the following complex-valued semilinear heat equation \begin{eqnarray*} \partial_t u = \Delta u + u^p, u \in \mathbb{C}, \end{eqnarray*} in the whole space $\mathbb{R}^n$, where $ p \in \mathbb{N}, p \geq 2$. We aim at cons
Externí odkaz:
http://arxiv.org/abs/1712.07183