Structural stability for a thermal convection model with temperature-dependent solubility

Global existence results for semi-linear structurally damped wave equations with nonlinear convection

In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term $ν(-Δ)^2 u_t$, where $ν>0$ is a constant. As being mentioned in [8,10], the linear principal part brings both the diffusion phenomenon and the regularity loss of solutions. This implies that, for the nonlinear problems, the choice of solution spaces plays an important role to obtain global solutions with sharp decay properties in time. Our main purpose of this paper is to prove the global (in time) existence of solutions for the small data and their decay properties for the supercritical n…

LRX-PINN：一种用于对流主导问题的具有集成柯西激活的层解析XNet物理信息神经网络

LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

针对对流主导的对流扩散问题中标准物理信息神经网络的结构不匹配，提出基于集成柯西激活的LRX-PINN，其结构匹配对流主导层缩放，实验表明该方法参数少精度高。