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pro vyhledávání: '"Kim, Seongyeon"'
We obtain well-posedness for Dirac equations with a Hartree-type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not addressed in previous st
Externí odkaz:
http://arxiv.org/abs/2308.09024
In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is related to Ph
Externí odkaz:
http://arxiv.org/abs/2308.03362
Autor:
Kim, Seongyeon, Saanouni, Tarek
This work studies the Cauchy problem for the energy-critical inhomogeneous Hartree equation with inverse square potential $$i\partial_t u-\mathcal K_\lambda u=\pm |x|^{-\tau}|u|^{p-2}(I_\alpha *|\cdot|^{-\tau}|u|^p)u, \quad \mathcal K_\lambda=-\Delta
Externí odkaz:
http://arxiv.org/abs/2305.00746
We discuss the Lugiato-Lefever equation and its variant with third-order dispersion, which are mathematical models used to describe how a light beam forms patterns within an optical cavity. It is mathematically demonstrated that the solutions of thes
Externí odkaz:
http://arxiv.org/abs/2304.10964
Adversarial training has been considered an imperative component for safely deploying neural network-based applications to the real world. To achieve stronger robustness, existing methods primarily focus on how to generate strong attacks by increasin
Externí odkaz:
http://arxiv.org/abs/2301.04785
Autor:
Kim, Seongyeon
We study the well-posedness for the inhomogeneous Hartree equation $i\partial_t u + \Delta u = \lambda(I_\alpha \ast |\cdot|^{-b}|u|^p)|x|^{-b}|u|^{p-2}u$ in $H^s$, $s\ge0$. Until recently, its well-posedness theory has been intensively studied, focu
Externí odkaz:
http://arxiv.org/abs/2212.07195
Autor:
Kim, Seongyeon
In this paper, we investigate the dichotomous behavior of solutions to the Kawahara equation with bounded variation initial data, analogous to the Talbot effect. Specifically, we observe that the solution is quantized at rational times, whereas at ir
Externí odkaz:
http://arxiv.org/abs/2208.06901
In this paper we obtain some new Strichartz estimates for the Dirac flow in the context of Wiener amalgam spaces which control the local regularity of a function and its decay at infinity separately unlike $L^p$ spaces. While it is well understood re
Externí odkaz:
http://arxiv.org/abs/2205.05547
We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in $L^2$, to which as time passes all solutions draw closer. In fact, we show that
Externí odkaz:
http://arxiv.org/abs/2205.04642
We study the Cauchy problem for the inhomogeneous Hartree equation in this paper. Although its well-posedness theory has been extensively studied in recent years, much less is known compared to the classical Hartree model of homogeneous type. In part
Externí odkaz:
http://arxiv.org/abs/2110.14922