On Schrödinger Equations with Concentrated Nonlinearities
نویسندگان
چکیده
منابع مشابه
Wave Equations with Concentrated Nonlinearities
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field V on an open subset of C and a discrete set Y ⊂ R with n elements, we define a nonlinear operator ∆V,Y on L (R) which coincides with the free Laplacian when restricted to regular functions vanishing at Y , and which reduces to the usual Laplacian with point interactions placed ...
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which suggests dissipativity if Imλ < 0. In fact, it is proved in [17] that the solution decays like O((t log t)−1/2) in Lx as t → +∞ if Imλ < 0 and u0 is small enough. Since the non-trivial free solution (i.e., the solution to (1) for N ≡ 0, u0 = 0) only decays like O(t−1/2), this gain of additional logarithmic time decay reflects a disspative character. Now we turn our attentions to the gener...
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ژورنال
عنوان ژورنال: Annals of Physics
سال: 1995
ISSN: 0003-4916
DOI: 10.1006/aphy.1995.1040