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- W4312397344 abstract "Abstract This work is concerned with a multi-dimensional viscoelastic pseudo-parabolic equation with critical Sobolev exponent. First, with some suitable conditions, we prove that the weak solution exists globally. Next, we show that the stability of the system holds for a much larger class of kernels than the ones considered in previous literature. More precisely, we consider the kernel <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>g</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mo stretchy=false>[</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>∞</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mspace width=0.33em /> <m:mo>⟶</m:mo> <m:mspace width=0.33em /> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>∞</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:math> g:{[}0,infty )hspace{0.33em}longrightarrow hspace{0.33em}(0,infty ) satisfying <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mrow> <m:mi>g</m:mi> </m:mrow> <m:mrow> <m:mo accent=true>′</m:mo> </m:mrow> </m:msup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo>⩽</m:mo> <m:mo>−</m:mo> <m:mi>ξ</m:mi> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mi>G</m:mi> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>g</m:mi> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mi>t</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:math> {g}^{^{prime} }(t)leqslant -xi (t)G(g(t)) , where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>ξ</m:mi> </m:math> xi and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>G</m:mi> </m:math> G are functions satisfying some specific properties." @default.
- W4312397344 created "2023-01-04" @default.
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- W4312397344 date "2022-01-01" @default.
- W4312397344 modified "2023-09-30" @default.
- W4312397344 title "General decay for a nonlinear pseudo-parabolic equation with viscoelastic term" @default.
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- W4312397344 doi "https://doi.org/10.1515/dema-2022-0164" @default.
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