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

Applicationes Mathematicae (2000)

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

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topRencławowicz, 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

top- [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
- [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
- [F1] H. Fujita, On the blowing up of solutions of the Cauchy problem for ${u}_{t}=u+{u}^{1}+\xe5l$, 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. Zbl1002.35070

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