Single blowup point for a semilinear reaction‐diffusion system
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DOI: 10.1002/mana.201400335
Abstract: Throughout this paper, we investigate the blowup set for the semilinear reaction‐diffusion system ut=Δu+f(u,v),x∈Ω,t>0,vt=Δv+g(u,v),x∈Ω,t>0,u(x,t)=v(x,t)=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω,where Ω=BR:={x∈Rn;|x| read more here.
Keywords: semilinear reaction; reaction diffusion; diffusion system; blowup ... See more keywords
“Local-in-space” Blowup Criterion for a Weakly Dissipative Dullin–Gottwald–Holm Equation
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DOI: 10.1007/s40840-020-01046-y
Abstract: We are concerned with the blowup phenomena of a dissipative Dullin–Gottwald–Holm equation which can describe unidirectional propagation of surface waves in a shallow water regime. A “local-in-space” blowup criterion is obtained by delicate analysis on… read more here.
Keywords: dullin gottwald; dissipative dullin; gottwald holm; holm equation ... See more keywords
Excluding blowup at zero points of the potential by means of Liouville-type theorems
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DOI: 10.1016/j.jde.2018.06.025
Abstract: We prove a local version of a (global) result of Merle and Zaag about ODE behavior of solutions near blowup points for subcritical nonlinear heat equations. As an application, for the equation $u_t= \Delta u+V(x)f(u)$,… read more here.
Keywords: points potential; type theorems; liouville type; blowup zero ... See more keywords
‘Life after death’ in ordinary differential equations with a non-Lipschitz singularity
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DOI: 10.1088/1361-6544/abbe60
Abstract: We consider a class of ordinary differential equations featuring a non-Lipschitz singularity at the origin. Solutions exist globally and are unique up until the first time they hit the origin. After ‘blowup’, infinitely many solutions… read more here.
Keywords: ordinary differential; lipschitz singularity; differential equations; non lipschitz ... See more keywords