Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations
نویسندگان
چکیده
منابع مشابه
Existence and Nonexistence of Global Solutions of Some Non-local Degenerate Parabolic Systems
This paper establishes a new criterion for global existence and nonexistence of positive solutions of the non-local degenerate parabolic system ut = v p ( ∆u+ a ∫
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where p,q > 1 and u(x,0) = u0(x), v(x,0) = v0(x), x ∈ R. Systems like (1.1) and (1.2) will be called degenerate and singular, respectively. Several authors have addressed this problem recently: we refer the interested reader to the papers by Levine [4] and Deng and Levine [1] for a survey of the literature on this subject. In the proofs we follow the technique developed by Mitidieri and Pohozae...
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This article presents necessary conditions for the existence of weak solutions of the following space-nonlocal evolution equations on H× (0, +∞), where H is the Heisenberg group: ∂2u ∂t2 + (−∆H)|u| = |u|, ∂u ∂t + (−∆H)|u| = |u|, ∂2u ∂t2 + (−∆H)|u| + ∂u ∂t = |u|, p ∈ R, p > 1, m ∈ N. Moreover, the life span for each equation is estimated under some suitable conditions. Our method of proof is bas...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2003
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(03)80118-0