The Quenching Behavior for a Quasilinear Parabolic Equation with Singular Source and Boundary Flux
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-018-9415-x
Abstract: In this paper, we consider the quenching behavior for a one-dimensional quasilinear parabolic equation with singular source and boundary flux. We show that the quenching occurs only on the boundary in finite time, and derive… read more here.
Keywords: singular source; parabolic equation; source boundary; quasilinear parabolic ... See more keywords
Global Existence, Extinction, and Non-Extinction of Solutions to a Fast Diffusion p-Laplace Evolution Equation with Singular Potential
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-019-09462-5
Abstract: In this paper, we study a class of fast diffusion p-Laplace equation with singular potential in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates, Hardy-Littlewood-Sobolev inequality, and some ordinary differential… read more here.
Keywords: diffusion laplace; fast diffusion; extinction; equation ... See more keywords
The Cahn–Hilliard–Oono equation with singular potential
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Models and Methods in Applied Sciences"
DOI: 10.1142/s0218202517500506
Abstract: We consider the so-called Cahn–Hilliard–Oono equation with singular (e.g. logarithmic) potential in a bounded domain of ℝd, d ≤ 3. The equation is subject to an initial condition and Neumann homogeneous boundary conditions for the… read more here.
Keywords: oono equation; cahn hilliard; hilliard oono; equation ... See more keywords
Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity
Sign Up to like & getrecommendations! Published in 2020 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2020042
Abstract: This paper concerns with a semilinear heat equation with singular potential and logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, the existence of global solutions and infinite time blow-up… read more here.
Keywords: semilinear heat; heat equation; equation singular; singular potential ... See more keywords