Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity

被引：3

作者：

Jaquette, Jonathan ^{[1
]}

Lessard, Jean-Philippe ^{[2
]}

Takayasu, Akitoshi ^{[3
]}

机构：

[1] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA

[2] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada

[3] Univ Tsukuba, Fac Engn Informat & Syst, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058573, Japan

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2022年 / 107卷

基金：

加拿大自然科学与工程研究理事会; 日本学术振兴会;

关键词：

Nonlinear heat equation; Heteroclinic connections; Global existence of solution; Rigorous numerics; PARAMETERIZATION METHOD; BLOW-UP; CRITICAL EXPONENTS; HEAT-EQUATION;

D O I：

10.1016/j.cnsns.2021.106188

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the dynamics of solutions to complex-valued evolutionary partial differential equations (PDEs) and show existence of heteroclinic orbits from nontrivial equilibria to zero via computer-assisted proofs. We also show that the existence of unbounded solutions along unstable manifolds at the equilibrium follows from the existence of heteroclinic orbits. Our computer-assisted proof consists of three separate techniques of rigorous numerics: an enclosure of a local unstable manifold at the equilibria, a rigorous integration of PDEs, and a constructive validation of a trapping region around the zero equilibrium. (C) 2021 The Authors. Published by Elsevier B.V.

引用

页数：14

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