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In this paper we study the global existence and uniqueness of solution for a Klein-Gordon equations system with mixed boundary conditions. Also we analyze the asymptotic behavior of this solution.

Analysis of PDEs · Mathematics 2019-10-24 Cládio O. P. Da Silva , Aldo T. Louredo , Manuel Milla Miranda

We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…

Analysis of PDEs · Mathematics 2020-02-26 Alexandru D. Ionescu , Benoit Pausader

In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…

Analysis of PDEs · Mathematics 2017-12-15 Yue MA

In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…

Analysis of PDEs · Mathematics 2023-12-07 Qian Zhang

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering…

Analysis of PDEs · Mathematics 2012-09-20 Tobias Schottdorf

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…

Analysis of PDEs · Mathematics 2012-08-14 Alexandru D. Ionescu , Benoit Pausader

In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…

Analysis of PDEs · Mathematics 2019-07-09 Yue Ma

We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c \geq 1$, which however…

Analysis of PDEs · Mathematics 2018-02-14 Stefano Pasquali

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…

Analysis of PDEs · Mathematics 2023-12-06 Xinyu Cheng

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global smooth…

Analysis of PDEs · Mathematics 2009-06-22 Axel Gruenrock , Hartmut Pecher

We are interested in the global solutions to a class of Klein-Gordon equations, and particularly in the unified time decay results with respect to the possibly vanishing mass parameter. We give for the first time a rigorous proof, which…

Analysis of PDEs · Mathematics 2019-05-22 Shijie Dong

We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses satisfying the resonance relation. We introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at…

Analysis of PDEs · Mathematics 2011-04-08 Yuichiro Kawahara , Hideaki Sunagawa

We consider a coupled Wave-Klein-Gordon system in 3D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch-Ma as a simplified…

Analysis of PDEs · Mathematics 2019-11-26 Alexandru D. Ionescu , Benoit Pausader

A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon…

Mathematical Physics · Physics 2013-11-08 R. Huegele , Z. E. Musielak , J. L. Fry

We consider the Cauchy problem of massless Dirac-Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be…

Analysis of PDEs · Mathematics 2016-03-02 Nicolas Ginoux , Olaf Müller

We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…

Analysis of PDEs · Mathematics 2025-11-20 Guocong Shang

In this {\bf draft version} we prove inhomogeneous Strichartz estimates with spherical symmetry in the abstract setting via duality arguments. Then we derive some new explicit estimates in the context of the wave equation. This allows us to…

Analysis of PDEs · Mathematics 2009-04-01 Evgeni Y Ovcharov

In this paper, the Cauchy problem for the multi-dimensional (M-D) bipolar Euler-Poisson equations with far field vacuum is considered. Based on physical observations and some elaborate analysis of this system's intrinsic symmetric…

Analysis of PDEs · Mathematics 2025-08-12 Zhongmin Qian , Liang Zhao , Shengguo Zhu

We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…

Analysis of PDEs · Mathematics 2019-05-28 Brian P. Cupps , Jeff Morgan , Bao Quoc Tang

We prove global well-posedness and scattering for the massive Dirac-Klein-Gordon system with small and low regularity initial data in dimension two. To achieve this, we impose a non-resonance condition on the masses.

Analysis of PDEs · Mathematics 2025-01-08 Ioan Bejenaru , Vitor Borges