Geodesic
GLOBAL EXISTENCE AND BLOW-UP FOR A DOUBLY DEGENERATE PARABOLIC EQUATION SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 309-324

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In this paper, we deal with the global existence and blow-up of solutions to a doubly degenerative parabolic system with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of non-negative solutions, which extend the recent results of Zheng, Song and Jiang (S. N. Zheng, X. F. Song and Z. X. Jiang, Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), 308–324), Xiang, Chen and Mu (Z. Y. Xiang, Q. Chen, C. L. Mu, Critical curves for degenerate parabolic equations coupled via nonlinear boundary flux, Appl. Math. Comput. 189 (2007), 549–559) and Zhou and Mu (J. Zhou and C. L Mu, On critical Fujita exponents for degenerate parabolic system coupled via nonlinear boundary flux, Pro. Edinb. Math. Soc. 51 (2008), 785–805) to more general equations.
DOI : 10.1017/S0017089511000619
Mots-clés : 35K55, 35K65, 35B40 
MI, YONG-SHENG; MU, CHUN-LAI; LIU, DENG-MING. GLOBAL EXISTENCE AND BLOW-UP FOR A DOUBLY DEGENERATE PARABOLIC EQUATION SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 309-324. doi: 10.1017/S0017089511000619
@article{10_1017_S0017089511000619,
     author = {MI, YONG-SHENG and MU, CHUN-LAI and LIU, DENG-MING},
     title = {GLOBAL {EXISTENCE} {AND} {BLOW-UP} {FOR} {A} {DOUBLY} {DEGENERATE} {PARABOLIC} {EQUATION} {SYSTEM} {WITH} {NONLINEAR} {BOUNDARY} {CONDITIONS}},
     journal = {Glasgow mathematical journal},
     pages = {309--324},
     year = {2012},
     volume = {54},
     number = {2},
     doi = {10.1017/S0017089511000619},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000619/}
}
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