Global existence and finite time blow-up of solutions of a Gierer-Meinhardt system

详细信息    查看全文

• 作者：Fang Li^a ; ^{fangli0214@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Rui Peng^b ; ^{pengrui_seu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xianfa Song^c ; ^{songxianfa@tju.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gierer&ndash ; Meinhardt system ; Global existence ; Finite time blow-up
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 January 2017
• 年：2017
• 卷：262
• 期：1
• 页码：559-589
• 全文大小：415 K

文摘

We are concerned with the Gierer–Meinhardt system with zero Neumann boundary condition: where rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si2.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=eccdbcedc1600e12c601cad7e75699b7" title="Click to view the MathML source">p>1r hidden">roll">p>1, rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si3.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=15b3183b91a40cf31a46eb53f25215ec" title="Click to view the MathML source">s>−1r hidden">roll">s>−1, rc">rce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si4.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=68954519f06eaa3bdcc7191080f4f240">rce" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022039616303138-si4.gif">ript>rder="0" style="vertical-align:bottom" width="125" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022039616303138-si4.gif">ript>r hidden">roll">q,r,row>drow>row>1row>,row>drow>row>2row>,row>arow>row>1row>,row>arow>row>2row> are positive constants, rc">rce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si5.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=786f5675b19b27d9c988e2f3e41f32f0">rce" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022039616303138-si5.gif">ript>rder="0" style="vertical-align:bottom" width="89" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022039616303138-si5.gif">ript>r hidden">roll">row>δrow>row>1row>,row>δrow>row>2row>,row>urow>row>0row>,row>vrow>row>0row> are nonnegative smooth functions, rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si6.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=89ce441b683e055992000ceb4291830c" title="Click to view the MathML source">Ω⊂R^dr hidden">roll">riant="normal">Ω⊂row>riant="double-struck">Rrow>row>drow> (rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si7.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=e3906d187430441582915461a5328cab" title="Click to view the MathML source">d≥1r hidden">roll">d≥1) is a bounded smooth domain. We obtain new sufficient conditions for global existence and finite time blow-up of solutions, especially in the critical exponent cases: rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si75.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=a2b130994e7a9dd576012c56b4ab5d5f" title="Click to view the MathML source">p−1=rr hidden">roll">p−1=r and rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022039616303138&_mathId=si9.gif&_user=111111111&_pii=S0022039616303138&_rdoc=1&_issn=00220396&md5=662242c9790f7f83b22b24bcb2055776" title="Click to view the MathML source">qr=(p−1)(s+1)r hidden">roll">qr=retchy="false">(p−1retchy="false">)retchy="false">(s+1retchy="false">).