Cauchy problems of semilinear pseudo-parabolic equations
Cauchy problems of semilinear pseudo-parabolic equations
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DOI：
10.1016/j.jde.2009.03.021
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发表时间：
2009-06-15
影响因子：
2.4
通讯作者：
Wang, Chunpeng
中科院分区：
文献类型：
--
作者：
Cao, Yang;Yin, Jingxue;Wang, Chunpeng
本文研究半线性拟抛物型方程的柯西问题。在建立了温解的存在唯一性和比较原理之后，在初始数据适当光滑的情况下，温解也是经典解，研究了解的大时间性态。证明了伪抛物方程仍然存在临界整体存在指数和临界Fujita指数，并且这两个临界指数与相应的半线性热方程是一致的。(C)2009 Elsevier Inc.保留所有权利。
This paper concerns with the Cauchy problems of semilinear pseudo-parabolic equations. After establishing the necessary existence, uniqueness and comparison principle for mild solutions, which are also classical ones provided that the initial data are appropriately smooth, we investigate large time behavior of solutions. It is shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations. (c) 2009 Elsevier Inc. All rights reserved.