Besov型时间加权框架下半线性波动方程的全局适定性和自相似性

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2020-03-01 DOI:10.1142/s0219891620500046

L. Ferreira, J. E. Pérez-López

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引用次数: 0

摘要

对于[公式:见文本]，我们在基于较大齐次Besov空间族[公式:见文本]的时间加权框架中，展示了具有非线性[公式:见文本]的半线性波动方程的全局时态适定性和自相似性。因此，在某些情况下[公式:见文本]，我们覆盖的初始数据类比之前的一些结果更大。我们的方法依赖于分散型估计和Besov空间中合适的[公式:见文本]-乘积估计。

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Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type

We show global-in-time well-posedness and self-similarity for the semilinear wave equation with nonlinearity [Formula: see text] in a time-weighted framework based on the larger family of homogeneous Besov spaces [Formula: see text] for [Formula: see text]. As a consequence, in some cases of the power [Formula: see text], we cover a initial-data class larger than in some previous results. Our approach relies on dispersive-type estimates and a suitable [Formula: see text]-product estimate in Besov spaces.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.