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Title: Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation

In this paper, we are concerned with the Cauchy problem of the inhomogeneous Hartree equation: iu{sub t}=−Δu−k(x)(∫{sub R{sup N}}(k(y))/(|x−y|{sup 2}) |u(t,y)|{sup 2}dy)u(t,x), x∈R{sup N}, N ⩾ 3. First, we establish the mass concentration property of the blow-up solutions. Second, we show that the blow-up solutions with minimal mass should concentrate at a critical point of k. Finally, under certain assumptions on global maximum points of k we establish nonexistence of such solutions.
Authors:
;  [1]
  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
Publication Date:
OSTI Identifier:
22250913
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CAUCHY PROBLEM; EQUATIONS; MASS; MATHEMATICAL SOLUTIONS