We study the global existence of solution to one di- mensional convection-diffusion equation. Through constructing a Cauchy sequence in a Banach space, we get the local existence of solution to the equation, t3ased on...We study the global existence of solution to one di- mensional convection-diffusion equation. Through constructing a Cauchy sequence in a Banach space, we get the local existence of solution to the equation, t3ased on the global bounds of the solu- tion, we extend the local one to a global one that decays in Hl space.展开更多
Let M be a compact Riemann surface, h（x） a positive smooth function on M, and Ф（x） a smooth function on M which satisfies that ∫MeФdVg = 1. In this paper, we consider the functionalJ（u）=1/2∫M｜△u｜2eФdVg＋...Let M be a compact Riemann surface, h（x） a positive smooth function on M, and Ф（x） a smooth function on M which satisfies that ∫MeФdVg = 1. In this paper, we consider the functionalJ（u）=1/2∫M｜△u｜2eФdVg＋8πc∫MueФ-8πclog∫Mheu＋ФdVg.We give a sufficient condition under which J achieves its minimum for c ≤ infx∈MeФ（X）.展开更多
基金Supported by the National Natural Science Foundation of China(11101121)
文摘We study the global existence of solution to one di- mensional convection-diffusion equation. Through constructing a Cauchy sequence in a Banach space, we get the local existence of solution to the equation, t3ased on the global bounds of the solu- tion, we extend the local one to a global one that decays in Hl space.
文摘Let M be a compact Riemann surface, h（x） a positive smooth function on M, and Ф（x） a smooth function on M which satisfies that ∫MeФdVg = 1. In this paper, we consider the functionalJ（u）=1/2∫M｜△u｜2eФdVg＋8πc∫MueФ-8πclog∫Mheu＋ФdVg.We give a sufficient condition under which J achieves its minimum for c ≤ infx∈MeФ（X）.
