ON THE CAUCHY PROBLEM FOR A SEMILINEAR NEWTON EQUATION OF MOTION DERIVED FROM A SEMILINEAR SCHRO DINGER EQUATION IN HOMOGENEOUS AND ISOTROPIC SPACETIMES

被引：0

作者：

Nakamura, Makoto ^{[1
]}

机构：

[1] Osaka Univ, Grad Sch Informat Sci & Technol, 1-5 Yamadaoka, Suita, Osaka 5650871, Japan

来源：

TSUKUBA JOURNAL OF MATHEMATICS | 2023年 / 47卷 / 02期

关键词：

Newton equation of motion; Cauchy problem; homogeneous and isotropic; spacetime; KLEIN-GORDON EQUATIONS; EMDEN-FOWLER TYPE; NONRELATIVISTIC LIMIT; ASYMPTOTIC-BEHAVIOR; POSITIVE SOLUTIONS; GLOBAL-SOLUTIONS; UNIQUENESS; FIELD;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A semilinear Newton equation of motion is derived from a semilinear Schrodinger equation in homogeneous and isotropic spacetimes by the Ehrenfest theorem. The Cauchy problem for the equation is considered, especially, on the existence of global solutions and nonexistence of global weak solutions. The effects of spatial expansion and contraction are studied.

引用

页码：153 / 189

页数：37

共 24 条

[1] Ambrosetti A., 1993, Progress in Nonlinear Differential Equations and their Applications, V10
[2] Asymptotic Behavior of Singular Solutions of Emden-Fowler Type Equations
Astashova, I. V.
[J]. DIFFERENTIAL EQUATIONS, 2019, 55 (05) : 581 - 590
[3] Astashova I. V., 2009, Funct. Differ. Equ., V16, P93
[4] Strichartz Estimates on Asymptotically de Sitter Spaces
Baskin, Dean
[J]. ANNALES HENRI POINCARE, 2013, 14 (02): : 221 - 252
[5] SOLVABILITY OF SEMILINEAR GRADIENT OPERATOR EQUATIONS
BERGER, MS
SCHECHTER, M
[J]. ADVANCES IN MATHEMATICS, 1977, 25 (02) : 97 - 132
[6] PERIODIC SOLUTIONS OF SECOND ORDER DYNAMICAL SYSTEMS AND ISOPERIMETRIC VARIATIONAL PROBLEMS
BERGER, MS
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1971, 93 (01) : 1 - &
[7] Carroll S.M., 2019, SPACETIME GEOMETRY
[8] DInverno R., 1992, Introducing Einstein's Relativity
[9] Global solutions for semilinear Klein-Gordon equations in FLRW spacetimes
Galstian, Anahit
Yagdjian, Karen
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 113 : 339 - 356
[10] Vertical asymptotes of solutions of the Emden-Fowler equation
Knezevic-Miljanovic, J.
[J]. DIFFERENTIAL EQUATIONS, 2007, 43 (12) : 1753 - 1755

← 1 2 3 →