具非局部源的伪抛物型方程的整体解与非整体解  

Global and Nonglobal Solutions for Pseudo-parabolic Equation with Nonlocal Source

作　　者：杨春晓[1] 高苗 樊婕妤 YANG Chunxiao;GAO Miao;FAN Jieyu(School of Science,Xi'an University of Architecture and Technology University,Xi'an,Shaanci,710055,P.R.China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《数学进展》2024年第4期849-860,共12页Advances in Mathematics（China）

基　　金：Supported by NSFC (No.11501438);Natural Science Basic Research Plan in Shaanxi Province of China (No.2018JQ1052)。

摘　　要：本文研究了半线性伪抛物方程ut=k△ut+||w(x)u||_(L^(q)(R^(n)))^((p-1))u^(r+1)(x,t)柯西问题的整体解与非整体解,其中权函数满足对足够大的|x|,w(x)~|x|-s.我们分别在w(x)∈Lq(R^(n))和w(x)∈L^(q)(R^(n))两种情形下考虑了问题的临界Fujita指数.并讨论了权函数w(x)~|x|^(-s)以及伪抛物参数k对解的影响.In this paper,we study the global and nonglobal solutions for the Cauchy problem with semilinear pseudo-parabolic equationut=k△ut+||w(x)u||_(L^(q)(R^(n)))^((p-1))u^(r+1)(x,t),where the weight function w(x)~|x|^(-s)for large|x|.To the both cases w(x)∈L^(q)(R^(n))and w(x)■L^(q)(R^(n)),the corresponding critical Fujita exponents were considered.It is shown that the weight function w(x)and the pseudo-parabolic parameter k effect the evolution of solutions.

关 键 词：伪抛物方程 非局部源 整体解 爆破 

分 类 号：O175.2[理学—数学]