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Global solutions of the exponential wave equation with small initial data
허형진 대한수학회 2013 대한수학회보 Vol.50 No.3
We study the initial value problem of the exponential wave equation in Rn+1 for small initial data. We shows, in the case of n = 1, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When n ≥ 2, a vector field method is applied to show the stability of a trivial solution Φ= 0.
Remarks on the gradient flow of $\alpha$ energy potential on the line
Hyojun An,허형진 대한수학회 2023 대한수학회논문집 Vol.38 No.4
We are interested in the gradient flow of $\alpha$ energy potential. We provide basic estimates and study asymptotic behaviors for the case $N=2, \ldots, 5$.