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

Joanna Rencławowicz

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 2, page 203-218
  • ISSN: 1233-7234

Abstract

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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 i t = Δ u i + u i + 1 p i , i = 1 , . . . , m - 1 , u m t = Δ u 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.

How to cite

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Rencławowicz, Joanna. "Global existence and blow-up for a completely coupled Fujita type system." Applicationes Mathematicae 27.2 (2000): 203-218. <http://eudml.org/doc/219268>.

@article{Rencławowicz2000,
abstract = {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.},
author = {Rencławowicz, Joanna},
journal = {Applicationes Mathematicae},
keywords = {length of existence time},
language = {eng},
number = {2},
pages = {203-218},
title = {Global existence and blow-up for a completely coupled Fujita type system},
url = {http://eudml.org/doc/219268},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Rencławowicz, Joanna
TI - Global existence and blow-up for a completely coupled Fujita type system
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 2
SP - 203
EP - 218
AB - 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.
LA - eng
KW - length of existence time
UR - http://eudml.org/doc/219268
ER -

References

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  1. [EH] M. Escobedo and M. A. Herrero, Boundedness and blow up for a semilinear reaction-diffusion system, J. Differential Equations 89 (1991), 176-202. Zbl0735.35013
  2. [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. Zbl0822.35068
  3. [F1] H. Fujita, On the blowing up of solutions of the Cauchy problem for u t = u + u 1 + å l , J. Fac. Sci. Univ. Tokyo Sect. IA Math. 13 (1966), 109-124. 
  4. [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. 
  5. [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. Zbl1002.35070

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