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math.AP2026
Sharp Lifespan Dichotomies and Threshold Phenomena for Semilinear Heat Equations Driven by the Logarithmic Laplacian
Huyuan Chen, Rui Chen, Daniel Hauer +1
We study nonnegative mild solutions of \[ \partial_tu+(-Î)^{\ln}u=f(u) \qquad \text{in }(0,T)\times\mathbb R^N, \] with initial datum \(u(0,\cdot)=μu_0\), \(μ>0\). Unlike the cl…
math.AP2026
Existence and nonexistence of solutions for fractional elliptic equations arising from closed MEMS model
Huyuan Chen, Jialei Jiang, Jun Wang
The objective of our paper is to investigate fractional elliptic equations of the form within a bounded domain , subject to zero Dirichlet bounda…