Existence and nonexistence of global solutions for a semilinear reaction-diffusion system

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• 作者：Lin-Lin Li^a ; Hong-Rui Sun^a ; ¹ ; ^{hrsun@lzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Quan-Guo Zhang^b
• 关键词：Classical solutions ; Global solutions ; Blow up ; Critical exponent
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：97-124
• 全文大小：473 K

文摘

This paper is concerned with the blow-up and global existence of nonnegative solutions to the following Cauchy problem where the constants lsi2" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si2.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=22365be02a51d1d203f95f20ca4b56cd" title="Click to view the MathML source">p,q>0lass="mathContainer hidden">lass="mathCode">low="scroll">p,q>0 and lsi108" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si108.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=cd69e8a28dcf5f5acdff2c1f01cc19bc" title="Click to view the MathML source">a(x)≩0lass="mathContainer hidden">lass="mathCode">low="scroll">alse">(xlse">)≩0 is on the order lsi4" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si4.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=bdaf7d5f3d9aac2beefe1bb750f84336" title="Click to view the MathML source">|x|^mlass="mathContainer hidden">lass="mathCode">low="scroll">lse">|xlse">|m as lsi249" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si249.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=c8fc607a5122d30d8b9aeb70e3a4e148" title="Click to view the MathML source">|x|→∞lass="mathContainer hidden">lass="mathCode">low="scroll">lse">|xlse">|lse">→∞, lsi6" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si6.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=c91e98619d25cfbd8fd7ded54f4f157e" title="Click to view the MathML source">m∈Rlass="mathContainer hidden">lass="mathCode">low="scroll">m∈le-struck">R. The Fujita critical exponent is determined when lsi7" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si7.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=772718e9553cef8e3a1e0fca211472b5" title="Click to view the MathML source">m≥0lass="mathContainer hidden">lass="mathCode">low="scroll">m≥0, and some results of global existence of solution under some assumptions when lsi159" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303912&_mathId=si159.gif&_user=111111111&_pii=S0022247X16303912&_rdoc=1&_issn=0022247X&md5=0b992a5f3cf599561200f2a9a7f63bee" title="Click to view the MathML source">m<0lass="mathContainer hidden">lass="mathCode">low="scroll">m<0 are also obtained. The results extend those in Escobedo and Herrero (1991) [9] and indicate that m affects the Fujita critical exponent.