Zobrazeno 1 - 10
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pro vyhledávání: '"35b44"'
Autor:
Jeong, Uihyeon, Kim, Taegyu
We consider the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS), an $L^2$-critical nonlinear Schr\"odinger type equation enjoying a number of numerous structures, such as nonlocal nonlinearity, self-duality, pseudo-conformal sym
Externí odkaz:
http://arxiv.org/abs/2412.12518
Autor:
Fioravanti, Gabriele
In this paper, we investigate the Dirichlet problem on lower dimensional manifolds for a class of weighted elliptic equations with coefficients that are singular on such sets. Specifically, we study the problem \[\begin{cases} -{\rm div}(|y|^a A(x,y)
Externí odkaz:
http://arxiv.org/abs/2412.11294
Autor:
Mao, Xuan, Li, Yuxiang
This paper is concerned with a three-component chemotaxis model accounting for indirect signal production, reading as $u_t = \nabla\cdot(\nabla u - u\nabla v)$, $v_t = \Delta v - v + w$ and $0 = \Delta w - w + u$, posed on a smoothly bounded domain $
Externí odkaz:
http://arxiv.org/abs/2412.10772
Autor:
Ikeda, Masahiro, Zhao, Jinhong
This article deals with the behavior in time of the solution to the Cauchy problem for a fractional wave equation with a weighted $L^1$ initial data. Initially, we establish the global existence of the solution using Fourier methods and provide upper
Externí odkaz:
http://arxiv.org/abs/2412.09155
Autor:
Fei, Qiang
We consider the existence problem of the following Singular Toda system on a compact Riemann surface $(\Sigma, g)$ without boundary \begin{equation*} \begin{cases} -\Delta_gu_1=2\overline{\rho}_1\Big({\frac{h_1e^{u_1}}{\int_{\Sigma}h_1e^{u_1}dV_g}}-1
Externí odkaz:
http://arxiv.org/abs/2412.08914
Autor:
Miller, Ian
In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schr\"{o}dinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some solutions wi
Externí odkaz:
http://arxiv.org/abs/2412.06962
Autor:
Quittner, Pavol
We consider a priori estimates of possibly sign-changing solutions to superlinear parabolic problems and their applications (blow-up rates, energy blow-up, continuity of blow-up time, existence of nontrivial steady states etc). Our estimates are base
Externí odkaz:
http://arxiv.org/abs/2412.05855
Autor:
Zhao, Yiheng
The Neumann problem in balls $\Omega\subset\mathbb{R}^n$, $n\in\{3,4\}$, for the chemotaxis system \begin{equation*} \left\{ \begin{array}{ll} u_t = \Delta u - \nabla \cdot (u\nabla v), \\[1mm] 0 = \Delta v - \mu^{(w)}(t) + w, \quad \mu^{(w)}(t) = \f
Externí odkaz:
http://arxiv.org/abs/2412.05909
Autor:
Shao, Kerun
We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and $\partial^{\leq\kappa}F(0)
Externí odkaz:
http://arxiv.org/abs/2412.05544
Autor:
Harada, Junichi
This paper investigates the asymptotic behavior of solutions to $u_t=\Delta u+|u|^{p-1}u$ in the Sobolev critical case. Our main result is a classification of the dynamics near the ground states in the six dimensional case. It is shown that solutions
Externí odkaz:
http://arxiv.org/abs/2412.04049