Singular limit in Hopf bifurcation for doubly diffusive convection equations II: bifurcation and stability

Singular limit in Hopf bifurcation for doubly diffusive convection equations I: linearized analysis at criticality

A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer for a parameters range where the Hopf bifurcation occurs in the corresponding incompressible system. The spectrum of the linearized operator in a time periodic function space is investigated in detail near the bifurcation point when the singular perturbation parameter is small. The results of this paper are the basis of the study of the nonlinear Hopf bifurcation problem and the singular limit of the time periodic bifurcating solu…

包含混合局部-非局部算子和对流项的双重非线性抛物型方程

Doubly nonlinear parabolic equation involving a mixed local-nonlocal operator and a convection term

本文研究了包含对流项与混合局部-非局部算子的双重退化抛物型方程，证明了弱-温和解的存在唯一性，并分析了其稳定化、灭绝与爆破行为对非线性条件的依赖。

具有非负散度奇异对流线性椭圆问题中 Hopf-Oleinik 引理的失效

Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence

本文研究了具有非负散度奇异对流的线性椭圆 Dirichlet 问题，将解的存在性理论推广至 $|E| \in L^2$ 并证明了比较原理，同时揭示此类奇异漂移项会导致 Hopf-Oleinik 引理失效。

Singular integral equations with applications to travelling waves for doubly nonlinear diffusion

We consider a family of singular Volterra integral equations that appear in the study of monotone travelling-wave solutions for a family of diffusion-convection-reaction equations involving the $p$-Laplacian operator. Our results extend the ones due to B.\,Gilding for the case $p=2$. The fact that $p\neq2$ modifies the nature of the singularity in the integral equation, and introduces the need to develop some new tools for the analysis. The results for the integral equation are then used to study the existence and properties of travelling-wave solutions for doubly nonlinear diffusion-reaction …

反应扩散方程锋面传播中产生的一个双重奇异边值问题的可解性

Solvability of a doubly singular boundary value problem arising in front propagation for reaction-diffusion equations

针对 $p$-Laplacian 型反应-扩散-对流方程行波研究中出现的含 $z^{-α}$ 奇性与零边值的双重奇异 ODE，本文在给定参数及连续系数条件下探讨其正解的可解性。