表面生长方程弱解的大时间行为

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-06-01 DOI:10.1063/5.0136559

Xuewen Wang, Chenggang Liu, Yanqing Wang, P. Han

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引用次数: 0

摘要

研究了表面生长方程弱解的存在性和衰减估计。首先，利用Majda和Bertozzi [Vorticity and Incompressible Flow (Cambridge University Press, 2001)]引入的近似方法，得到弱解的全局存在性。然后，在假设u0∈L1(R)∩L2(R)的前提下，通过傅里叶分裂方法导出弱解的L2衰减率。对于更一般的情况，即u0∈L2(R)，利用自伴随算子的谱理论得到了L2中弱解的性质。

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Large time behavior of weak solutions to the surface growth equation

This paper studies the existence and decay estimates of weak solutions to the surface growth equation. First, the global existence of weak solutions is obtained by the approximation method introduced by Majda and Bertozzi [Vorticity and Incompressible Flow (Cambridge University Press, 2001)]. Then, we derive the L2-decay rates of weak solutions via the Fourier splitting method under the assumption that u0∈L1(R)∩L2(R). For more general cases, i.e., u0∈L2(R), the behavior of weak solutions in L2 is obtained by the spectral theory of self-adjoint operators.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.