Now showing items 1-2 of 2

    • Catenoidal layers for the Allen-Cahn equation in bounded domains 

      Agudelo, Oscar; Pino Manresa, Manuel del; Wei, Juncheng (Springer, 2017)
      This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation α2Δu + u(1 − u2) = 0 in a smooth bounded domain Ω ⊂ R3, with Neumann boundary condition and α > 0 a small parameter. These ...
    • Solutions with multiple catenoidal ends to the Allen–Cahn equation in R3 

      Agudelo, Oscar; Pino Manresa, Manuel del; Wei, Juncheng. (Elsevier, 2015)
      We consider the Allen–Cahnequation Δu+u(1−u2)=0inR3. We construct two classes of axially symmetric solutions u=u(|x |,x3)suchthat the (multiple) components of the zero set look for large |x |like catenoids, namely|x3|∼Alog|x ...