A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations
Levine, Howard
Banach Center Publications, Tome 37 (1996), p. 193-198 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1996-01-01
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     author = {Levine, Howard},
     title = {A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations},
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {193-198},
     zbl = {0855.35072},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p193bwm}
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Levine, Howard. A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations. Banach Center Publications, Tome 37 (1996) pp. 193-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv33z1p193bwm/

[000] [A1] D. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), 890-896. | Zbl 0153.42002

[001] [A2] D. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scoula Norm. Sup. Pisa 6 (1968), 607-694. | Zbl 0182.13802

[002] [AW] D. Aronson and H. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978), 33-76. | Zbl 0407.92014

[003] [EH] M. Escobedo and M. A. Herrero, Boundedness and blowup for a semilinear reaction-diffusion system, J. Differential Equations 89 (1991), 176-202. | Zbl 0735.35013

[004] [FLU] M. Fila, H. A. Levine and Y. Uda, A Fujita type global existence-global nonexistence theorem for a system of reaction diffusion equations with differing diffusivities, Math. Methods Appl. Sci. 19 (1994), 809-835. | Zbl 0814.35046

[005] [Fu] H. Fujita, On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 16 (1966), 105-113.

[006] [L1] H. A. Levine, A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations, Z. Angew. Math. Phys. 42 (1992), 408-430. | Zbl 0786.35075

[007] [L2] H. A. Levine, The role of critical exponents in blow up theorems, SIAM Rev. 32 (1990), 262-288.

[008] [N] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954. | Zbl 0096.06902

[009] [U1] Y. Uda, The critical exponent for a weakly coupled system of generalized Fujita type reaction-diffusion equations, manuscript. | Zbl 0835.35071

[010] [U2] Y. Uda, Fujita type global existence-global nonexistence theorems for weakly coupled systems of reaction-diffusion equations, PhD dissertation, Iowa State University, 1993.

[011] [W] F. B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981), 29-40. | Zbl 0476.35043