Zobrazeno 1 - 10
of 228
pro vyhledávání: '"45g05"'
Autor:
Dolce, Michele, Grande, Ricardo
In this paper, we consider the long-term behavior of some special solutions to the Wave Kinetic Equation (WKE). This equation provides a mesoscopic description of wave systems interacting nonlinearly via the cubic NLS equation. Escobedo and Vel\'azqu
Externí odkaz:
http://arxiv.org/abs/2404.14400
We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in presence of a singular term. We use conformal transformations to rewrite the linearized equation as a Steklov eigenvalue proble
Externí odkaz:
http://arxiv.org/abs/2404.14119
Autor:
Shen, Zifei, Zhang, Shuijin
This paper studies the nonlinear fractional Helmholtz equation \begin{equation}\label{main} (-\Delta)^{s} u-k^{2} u=Q(x)|u|^{p-2}u, ~~\mathrm{in}~~\mathbb{R}^{N},~~N\geq3, \end{equation} where $\frac{N}{N+1}
Externí odkaz:
http://arxiv.org/abs/2312.15009
This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estimate for the exact solution via analyzing the associated convolution st
Externí odkaz:
http://arxiv.org/abs/2308.16696
Autor:
Deb, Sudip, Das, Anupam
In this study , we display a generalization of Darbos fixed point theorem , by using the use of a freshly made contraction operator and that we use to study the solvability of an integral equation involving the weighted fractional integral with respe
Externí odkaz:
http://arxiv.org/abs/2306.08922
Autor:
Grube, Florian, Kassmann, Moritz
We prove trace and extension results for Sobolev-type function spaces that are well suited for nonlocal Dirichlet and Neumann problems including those for the fractional $p$-Laplacian. Our results are robust with respect to the order of differentiabi
Externí odkaz:
http://arxiv.org/abs/2305.05735
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of solutions i
Externí odkaz:
http://arxiv.org/abs/2303.06449
Autor:
Alonso, Ricardo J., Gamba, Irene M.
This manuscript focus on an extensive survey with new techniques on the problem of solving the Boltzmann flow by bringing a unified approach to the Cauchy problem to homogeneous kinetic equations with Boltzmann-like collision operators under integrab
Externí odkaz:
http://arxiv.org/abs/2211.09188
The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades transferring for
Externí odkaz:
http://arxiv.org/abs/2208.00947
Autor:
Moon, Jun
In this paper, we study the optimal control problem with terminal and inequality state constraints for state equations described by Volterra integral equations having singular and nonsingular kernels. The singular kernel introduces abnormal behavior
Externí odkaz:
http://arxiv.org/abs/2203.05165