Existence, uniqueness, and blow-up rate of large solutions to equations involving the ∞−Laplacian on the half line

2017 ◽  
Vol 40 (12) ◽  
pp. 4577-4594
Author(s):  
Yujuan Chen ◽  
Li Chen
Keyword(s):  
Blow Up ◽  
Half Line ◽  
Solutions To Equations ◽  
Large Solutions ◽  
Blow Up Rate

scholarly journals The boundary blow-up rate of large solutions

2003 ◽  
Vol 195 (1) ◽  
pp. 25-45 ◽  
Author(s):  
Julián López-Gómez
Keyword(s):  
Blow Up ◽  
Large Solutions ◽  
Blow Up Rate

scholarly journals A nonlinear diffusion equation with reaction localized in the half-line

2021 ◽  
Vol 4 (3) ◽  
pp. 1-24
Author(s):  
Raúl Ferreira ◽  
◽  
Arturo de Pablo ◽  
Keyword(s):  
Global Existence ◽  
Diffusion Equation ◽  
Heat Equation ◽  
Nonlinear Diffusion ◽  
Blow Up ◽  
Nonlinear Diffusion Equation ◽  
Half Line ◽  
Blow Up Rate ◽  
Global Reaction

<abstract><p>We study the behaviour of the solutions to the quasilinear heat equation with a reaction restricted to a half-line</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_t = (u^m)_{xx}+a(x) u^p, $\end{document} </tex-math></disp-formula></p> <p>$ m, p &gt; 0 $ and $ a(x) = 1 $ for $ x &gt; 0 $, $ a(x) = 0 $ for $ x &lt; 0 $. We first characterize the global existence exponent $ p_0 = 1 $ and the Fujita exponent $ p_c = m+2 $. Then we pass to study the grow-up rate in the case $ p\le1 $ and the blow-up rate for $ p &gt; 1 $. In particular we show that the grow-up rate is different as for global reaction if $ p &gt; m $ or $ p = 1\neq m $.</p></abstract>

scholarly journals Existence and blow-up rate of large solutions of p(x)-Laplacian equations with gradient terms

2018 ◽  
Vol 457 (1) ◽  
pp. 944-977 ◽  
Author(s):  
Jingjing Liu ◽  
Patrizia Pucci ◽  
Haitao Wu ◽  
Qihu Zhang
Keyword(s):  
Blow Up ◽  
Large Solutions ◽  
Blow Up Rate ◽  
Laplacian Equations
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