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We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…

Analysis of PDEs · Mathematics 2020-04-30 Yavar Kian , Masahiro Yamamoto

In this paper, we consider the initial-boundary value problem of the 3D primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal…

Analysis of PDEs · Mathematics 2014-06-10 Chongsheng Cao , Jinkai Li , Edriss S. Titi

We consider the Cauchy problem for one-dimensional dispersive equations with a general nonlinearity in the periodic setting. Our main hypotheses are both that the dispersive operator behaves for high frequencies as a Fourier multiplier by $…

Analysis of PDEs · Mathematics 2022-03-31 Luc Molinet , Tomoyuki Tanaka

In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated.…

Analysis of PDEs · Mathematics 2024-06-26 Zihan Yin , Jing Kang , Xiaochuan Liu , Changzheng Qu

In this paper we are concerned with a initial boundary-value problem for a coupled system of two KdV equations, posed on the positive half line, under the effect of a localized damping term. The model arises when modeling the propagation of…

Analysis of PDEs · Mathematics 2012-12-10 Ademir Fernando Pazoto , Gilmar dos Reis Souza

Let T be an ergodic automorphism of the d-dimensional torus. In the spirit of Le Borgne, we give conditions on the Fourier coeffi cients of a real valued function f under which the Birkhoff sums satis fy a strong invariance principle. Next,…

Dynamical Systems · Mathematics 2012-06-21 Jérôme Dedecker , Florence Merlevède , Francoise Pene

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

Analysis of PDEs · Mathematics 2010-12-08 Heinz-Otto Kreiss , Omar E. Ortiz , N. Anders Petersson

We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…

Classical Analysis and ODEs · Mathematics 2018-08-24 N. D. Cong , T. S. Doan , H. T. Tuan

Given sufficiently regular data \textit{without} decay assumptions at infinity, we prove local well-posedness for non-linear dispersive equations of the form \[ \partial_t u + \mathsf A(\nabla) u + \mathcal Q(|u|^2) \cdot \nabla u= \mathcal…

Analysis of PDEs · Mathematics 2024-09-10 Jason Zhao

This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…

Numerical Analysis · Mathematics 2015-03-24 Roberto Garrappa , Marina Popolizio

We consider the initial value problem for the Navier-Stokes equations over $R^{3} \times [0,T]$ with a positive time $T$ in the spatially periodic setting. Identifying periodic vector-valued functions on $R^{3}$ with functions on the…

Analysis of PDEs · Mathematics 2021-06-10 Alexander Shlapunov , Nikolai Tarkhanov

The explicit solution of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODE s with second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary (time-independent)…

Dynamical Systems · Mathematics 2021-08-19 Francesco Calogero , Farrin Payandeh

This paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three-body problem. Near the Lagrangian equilibrium $\mathcal{L}_4$ a twistless…

Mathematical Physics · Physics 2015-06-17 Holger R Dullin , Joachim Worthington

An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on an unbounded domain is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data…

Analysis of PDEs · Mathematics 2017-04-18 Nikolai Larkin , Marcos Padilha

As a sequel to the paper [9], we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward-backward parabolic equations with diffusion fluxes violating Fourier's inequality.

Analysis of PDEs · Mathematics 2016-02-19 Seonghak Kim , Baisheng Yan

In this work we study a dispersive equation with a dissipative term, the Benjamin-Bona-Mahony-Burgers equation. First we prove that the initial value problem for this equation is well-posed in $H^s(\mathbb{R}),$ for $s\geq 0$ and ill-posed…

Analysis of PDEs · Mathematics 2012-07-30 Carlos Banquet Brango

This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic…

Analysis of PDEs · Mathematics 2014-01-14 Khaled El-Ghaouti Boutarene

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

Classical Analysis and ODEs · Mathematics 2007-05-23 C. A. Terrero-Escalante

We prove, under suitable non-resonance and non-degeneracy ``twist'' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic…

Dynamical Systems · Mathematics 2007-05-23 Massimiliano Berti , Luca Biasco , Enrico Valdinoci

We study the fourth-order stability of the triangular libration points in the absence of resonance for the three-body problem when the infinitesimal mass is affected not only by gravitation but also by light pressure from both primaries. A…

Earth and Planetary Astrophysics · Physics 2012-12-11 M. Alvarez-Ramírez , J. K. Formiga , R. V. de Moraes , J. E. F. Skea , T. J. Stuchi