Hasil untuk "math.AP"

Kosuzu Hamaoka, Keiichi Kato, Shun Takizawa

In this paper we give an estimate for the solution to the Schrödinger equation with sub-quadratic potentials in modulation spaces by the norm of the initial functions in Wiener-Amalgum spaces.

Yucong Huang, Aram Karakhanyan

The aim of this paper is to discuss some well known explicit examples of the three dimensional inviscid flows with free boundary constructed by John \cite{John} and Ovsyannikov \cite{Ovsyannikov}, and provide a detailed analysis of its long time behaviour.

Chutian Ma

In this paper, we study the cubic defocusing nonlinear wave equation on the three dimensional hyperbolic space. We use the Fourier truncation method to show that the equation is globally well-posed and scatters if the initial data lies in $H^s(\mathbb{H}^3)$, $s>\frac{182}{201}\approx 0.905$.

N. V. Krylov

We prove existence and uniqueness of solutions in Morrey spaces of functions with mixed norms for second-oder parabolic equations in the whole space with VMO $a$ and Morrey $b,c$.

Helge Dietert

The recent work [11] developed a general framework to show hypocoercivity for a stationary Gibbs state and allowed spatial degeneracy, confining potentials and boundary conditions. In this work, we show that the explicit energy approach in the weighted L$^2$ space works for general non-equilibrium steady states and that it can be adapted to cases with weaker confinement leading to algebraic decay.

Francesco Esposito, Berardino Sciunzi, Nicola Soave

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.

Kazuhiro Ishige

The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for nonnegative, bounded measurable initial functions with compact support.

Qiaohua Yang

We determine the optimal constant in the $L^{2}$ Folland-Stein inequality on the H-type group, which partially confirms the conjecture given by Garofalo and Vassilev (Duke Math. J., 2001). The proof is inspired by the work of Frank and Lieb (Ann. of Math., 2012) and Hang and Wang.

Nurdan Kar

In this paper, we establish the occurrence of blow-up in the time-fractional term at the quenching point. By demonstrating that the quenching points are contained within a compact subset of the designated spatial interval, we employ this finding to prove the blow-up of the Caputo fractional time-derivative at the quenching point.

Tim Van Hoose

We prove sharp $L^\infty$ decay and modified scattering for the Schrödinger-Bopp-Podolsky equation in $2$ and $3$ spatial dimensions with small initial data chosen from a weighted Sobolev space.

Weike Yu

In this note, we prove an existence result for generalized Kazdan-Warner equations on compact Riemannian manifolds by using the flow approach or the upper and lower solution method. In addition, we give a prior estimate for this type equations.

Mongi Blel, Jamel Benameur

We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).

Yuzhou Fang, Chao Zhang

We consider a class of generalized nonlocal $p$-Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solutions to such nonlocal problems by using the expansion of positivity and energy estimates.

Christoph Walker

Schauder's fixed point theorem is used to derive the existence of solutions to a semilinear heat equation. The equation features a nonlinear term that depends on the time-integral of the unknown on the whole, a priori given, interval of existence.

Yuhua Sun, Yadong Zheng

We investigate the non-existence and existence of positive solutions to biharmonic elliptic inequalities on manifolds. Using Green function and volume growth conditions, we establish the critical exponent for biharmonic problem.

Siming He

In this paper, we investigate a coupled Patlak-Keller-Segel-Navier-Stokes (PKS-NS) system. We show that globally regular solutions with arbitrary large cell populations exist. The primary blowup suppression mechanism is the shear flow mixing induced enhanced dissipation phenomena.

Claudianor O. Alves, Chao Ji

In this paper, we study the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with the potential in $\mathbb{R}^2$ via the variational methods.

Jörg Seiler

We study cone differential operators on the half-axis and edge-degenerate differential operators on a half-space. We construct subspaces of edge Sobolev spaces that can be considered as natural domains for edge-degenerate operators and indicate how they can be used in the study of boundary problems for edge-degenerate operators.

Ugo Bessi, Daniel Massart

We prove Mañé's conjectures in the context of codimension one Aubry-Mather theory

M. Arisawa

The equivalence of three different definitions of viscosity solutions for the integro-differential equation with the L{é}vy operator is shown in this paper. The key is Lemma 2.1, in which we construct a sequence of the approximating test functions.