Global existence and blow-up for a completely coupled Fujita type system

• Autorzy: Joanna Rencławowicz
• Języki publikacji: EN

Abstrakty

EN

The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form $u_{it} = Δu_i + u_{i+1}^{p_i}, i=1,..., m-1,$ $u_{mt} = Δu_m + u_1^{p_m}, x ∈ ℝ^N, t > 0,$ with nonnegative, bounded, continuous initial values and positive numbers $p_i$. The dependence on $p_i$ of the length of existence time (its finiteness or infinitude) is established.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 2
• Strony: 203-218

Daty

wydano

2000

otrzymano

1999-08-04

Twórcy

autor

Joanna Rencławowicz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [EH] M. Escobedo and M. A. Herrero, Boundedness and blow up for a semilinear reaction-diffusion system, J. Differential Equations 89 (1991), 176-202.
• [EL] M. Escobedo and H. A. Levine, Critical blow up and global existence numbers for a weakly coupled system of reaction-diffusion equations, Arch. Rational Mech. Anal. 129 (1995), 47-100.
• [F1] H. Fujita, On the blowing up of solutions of the Cauchy problem for $u_t = \tr u + u^1+ål$, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 13 (1966), 109-124.
• [F2] H. Fujita, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, in: Proc. Sympos. Pure Math. 18, Amer. Math. Soc., 1970, 105-113.
• [R] J. Rencławowicz, Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations, Appl. Math. (Warsaw) 25 (1998), 313-326.