Weakly coupled reaction–diffusion systems with rapidly growing nonlinearities and singular initial data

We study existence and nonexistence of a local in time solution for the weakly coupled reaction–diffusion system ∂tu=Δu+g(v)inRN×(0,T),∂tv=Δv+f(u)inRN×(0,T),(u(x,0),v(x,0))=(u0(x),v0(x))inRN,where f(u) and g(v) grow rapidly, u0 and v0 are possibly unbounded nonnegative initial functions in RN (N≥1)...

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Veröffentlicht in:	Nonlinear analysis 2019-12, Vol.189, p.111576, Article 111576
Hauptverfasser:	Miyamoto, Yasuhito, Suzuki, Masamitsu
Format:	Artikel
Sprache:	eng
Schlagworte:	Existence and nonexistence Local in time solutions Superexponential nonlinearity Weakly coupled parabolic system
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