Boundedness of solutions to a quasilinear chemotaxis-haptotaxis model

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• 作者：Jiashan Zheng^a ; ^{zhengjiashan2008@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yifu Wang^b
• 关键词：Boundedness ; Chemotaxis&ndash ; haptotaxis ; Global existence ; Logistic source
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：71
• 期：9
• 页码：1898-1909
• 全文大小：411 K

文摘

We study global solutions of a class of chemotaxis&ndash;haptotaxis systems generalizing the prototype in a bounded domain hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si2.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=276dc2c573b078aa95dfdc8051e872b7" title="Click to view the MathML source">Ω⊂R^N(N≥1)hContainer hidden">hCode">h altimg="si2.gif" overflow="scroll">Ω⊂hvariant="double-struck">RN(N≥1)h> with smooth boundary, hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si3.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=96e3776669fb04c049e89e4f0153ac91" title="Click to view the MathML source">H(u,w):=u(1−u^r−1−w)hContainer hidden">hCode">h altimg="si3.gif" overflow="scroll">H(u,w):=u(1−ur−1−w)h>, with parameters hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si4.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=27d69b475f9c50205a0756ffee062ba9" title="Click to view the MathML source">m≥1,r>1hContainer hidden">hCode">h altimg="si4.gif" overflow="scroll">m≥1,r>1h> and positive constants hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si5.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=cc38ce911e611a96a75e711258ef25c8" title="Click to view the MathML source">p,qhContainer hidden">hCode">h altimg="si5.gif" overflow="scroll">p,qh>. It is shown that either hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si6.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=5fa755e37bcea2d396173fd53ed4caa5">height="21" width="275" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0898122116301304-si6.gif">hContainer hidden">hCode">h altimg="si6.gif" overflow="scroll">max{q+1,p,2p−m}<max{m+2N,r}h> or hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si7.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=cea210045169e7c4036d4ec4368ef08b" title="Click to view the MathML source">max{q+1,p,2p−m}=rhContainer hidden">hCode">h altimg="si7.gif" overflow="scroll">max{q+1,p,2p−m}=rh> and hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116301304&_mathId=si8.gif&_user=111111111&_pii=S0898122116301304&_rdoc=1&_issn=08981221&md5=28404ff10beec78d9a1acb5693b38291" title="Click to view the MathML source">b>0hContainer hidden">hCode">h altimg="si8.gif" overflow="scroll">b>0h> is large enough, then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded. The results of this paper improve the results of Tao and Winkler (2014) [46,51].