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• W3191627424 abstract "In this paper, we consider the following indirect signal generation and singular sensitivity <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mfenced open={ close=> <mrow> <mtable class=cases> <mtr> <mtd columnalign=left> <msub> <mrow> <mi>n</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>Δ</mi> <mi>n</mi> <mo>+</mo> <mi>χ</mi> <mrow> <mo>∇</mo> </mrow> <mrow> <mo>⋅</mo> </mrow> <mfenced open=( close=)> <mrow> <mi>n</mi> <mo>/</mo> <mi>φ</mi> <mfenced open=( close=)> <mrow> <mi>c</mi> </mrow> </mfenced> <mo>∇</mo> <mi>c</mi> </mrow> </mfenced> <mo>,</mo> <mtext> </mtext> <mi>x</mi> <mo>∈</mo> <mi>Ω</mi> <mo>,</mo> <mi>t</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=left> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>Δ</mi> <mi>c</mi> <mo>−</mo> <mi>c</mi> <mo>+</mo> <mi>w</mi> <mo>,</mo> <mtext> </mtext> <mi>x</mi> <mo>∈</mo> <mi>Ω</mi> <mo>,</mo> <mi>t</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd columnalign=left> <msub> <mrow> <mi>w</mi> </mrow> <mrow> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>Δ</mi> <mi>w</mi> <mo>−</mo> <mi>w</mi> <mo>+</mo> <mi>n</mi> <mo>,</mo> <mtext> </mtext> <mi>x</mi> <mo>∈</mo> <mi>Ω</mi> <mo>,</mo> <mi>t</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mfenced> </math> in a bounded domain <math xmlns=http://www.w3.org/1998/Math/MathML id=M2> <mi>Ω</mi> <mo>⊂</mo> <msup> <mrow> <mi>R</mi> </mrow> <mrow> <mi>N</mi> </mrow> </msup> <mfenced open=( close=)> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </mfenced> </math> with smooth boundary <math xmlns=http://www.w3.org/1998/Math/MathML id=M3> <mi>∂</mi> <mi>Ω</mi> </math> . Under the nonflux boundary conditions for <math xmlns=http://www.w3.org/1998/Math/MathML id=M4> <mi>n</mi> </math> , <math xmlns=http://www.w3.org/1998/Math/MathML id=M5> <mi>c</mi> </math> , and <math xmlns=http://www.w3.org/1998/Math/MathML id=M6> <mi>w</mi> </math> , we first eliminate the singularity of <math xmlns=http://www.w3.org/1998/Math/MathML id=M7> <mi>φ</mi> <mfenced open=( close=)> <mrow> <mi>c</mi> </mrow> </mfenced> </math> by using the Neumann heat semigroup and then establish the global boundedness and rates of convergence for solution." @default.
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• W3191627424 date "2021-07-30" @default.
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• W3191627424 title "Boundedness and Asymptotic Behavior to a Chemotaxis System with Indirect Signal Generation and Singular Sensitivity" @default.
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