Analysis reveals stability and well-posedness in degenerate Schrödinger equations under boundary control implications.
This paper is devoted to study the well-posedness and stability of degenerate Schrödinger equation with a boundary control acting at the degeneracy. First, we establish the well-posedness of the degenerate problem vₜ(x,t)+(x^αvₓ(x,t))ₓ=0, with x ∈ (0,1), controlled by Dirichlet-Neumann conditions. Then, exponential and polynomial decreasing of the solution are established. This result is optimal and it is obtained using complex analysis method.
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Fekirini et al. (2025) studied this question.
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