Asymptotic behavior of solutions for evolution equations involving nonlinear Laplacians

点击翻译按钮获取中文摘要

In various nonlinear problems, we often encounter nonlinear elliptic operators as modified forms of the classical (linear) Laplacian. In this research, we consider evolution equations governed by such nonlinear operators and investigate asymptotic behavior of solutions and their mechanism. More precisely, we revealed long-time behavior of solutions for diffusion-type equations involving p(x)-Laplacians with variable exponents and the infinity-Laplacian, and moreover, we also established a novel theory of stability analysis of asymptotic profiles for vanishing (in finite time) solutions of fast diffusion equations.