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- W4306643536 abstract "Abstract The Neumann problem for (0.1)$$ begin{align}& V_t = Delta V-aV+f(x,t) end{align}$$is considered in bounded domains $Omega subset {mathbb {R}}^n$ with smooth boundary, where $nge 1$ and $ain {mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ begin{eqnarray*} sup_{tin (0,T)} int_Omega big|nabla V(cdot,t)big|^p L^{frac{n+p}{n+2}} Big( big|nabla V(cdot,t)big| Big) end{eqnarray*}$$in dependence on the expressions (0.2)$$ begin{align}& sup_{tin (0,T-tau)} int_t^{t+tau} int_Omega |f|^{frac{(n+2)p}{n+p}} Lbig( |f|big) end{align}$$is derived for $pge 2$, $tau>0$, and $Tge 2tau $, provided that $Lin C^0([0,infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $limsup _{sto infty } frac {L(s^{lambda _0})}{L(s)} <infty $ for some $lambda _0>1$. In the particular case when $p=nge 2$, an additional condition on growth of $L$, particularly satisfied by $L(xi ):=ln ^alpha (xi +b)$ whenever $b>0$ and $alpha>frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ begin{eqnarray*} left{ begin{array}{l} u_t = nabla cdot big( D(v)nabla ubig) - nabla cdot big( uS(v)nabla vbig) + ru - mu u^2, [1mm] v_t = Delta v-v+u, end{array} right. end{eqnarray*}$$shows that when $n=2$, $rin {mathbb {R}}$, $0<Din C^2([0,infty ))$, and $Sin C^2([0,infty )) cap W^{1,infty }((0,infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $mu>0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution." @default.
- W4306643536 created "2022-10-18" @default.
- W4306643536 creator A5041353240 @default.
- W4306643536 date "2022-10-13" @default.
- W4306643536 modified "2023-10-10" @default.
- W4306643536 title "A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System" @default.
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- W4306643536 cites W1978851480 @default.
- W4306643536 cites W1981587125 @default.
- W4306643536 cites W1990021158 @default.
- W4306643536 cites W1994772198 @default.
- W4306643536 cites W2007430988 @default.
- W4306643536 cites W2009746295 @default.
- W4306643536 cites W2012474375 @default.
- W4306643536 cites W2021117151 @default.
- W4306643536 cites W2021427241 @default.
- W4306643536 cites W2035308163 @default.
- W4306643536 cites W2052129269 @default.
- W4306643536 cites W2056289252 @default.
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- W4306643536 cites W2073873819 @default.
- W4306643536 cites W2076491113 @default.
- W4306643536 cites W2078125833 @default.
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- W4306643536 cites W2138620270 @default.
- W4306643536 cites W2142491793 @default.
- W4306643536 cites W2146630187 @default.
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- W4306643536 doi "https://doi.org/10.1093/imrn/rnac286" @default.
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