References
- Anderson , JR and Deng , K . 1997 . Global existence for degenerate parabolic equations with a nonlocal forcing . Math. Methods Appl. Sci. , 20 : 1069 – 1087 .
- Deng , W , Li , Y and Xie , C . 2003 . Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations . App. Math. Lett. , 16 : 803 – 808 .
- Deng , W , Li , Y and Xie , C . 2003 . Global existence and nonexistence for a class of degenerate parabolic systems . Nonlinear Anal. , 55 : 233 – 244 .
- Furter , J and Grinfeld , M . 1989 . Local vs nonlocal interactions in population dynamics . J. Math. Biol. , 27 : 65 – 80 .
- Souplet , P . 1998 . Blow up in nonlocal reaction-diffusion equations . SIAM J. Math. Anal. , 29 : 1301 – 1334 .
- Bebernes , J and Bressan , A . 1982 . Thermal behavior of a confined reactive gas . J. Differ. Equ. , 44 : 118 – 133 .
- Bebernes , J , Bressan , A and Lacey , A . 1988 . Total blow up versus single point blow up . J. Differ. Equ. , 73 : 30 – 44 .
- Chen , Y and Gao , H . 2007 . Asymptotic blow-up behavior for a nonlocal degenerate parabolic equation . J. Math. Anal. Appl. , 330 : 852 – 863 .
- Chen , Y and Wang , MX . 2009 . A class of nonlocal and degenerate quasilinear parabolic system not in divergence form . Nonlinear Anal. , 71 : 3530 – 3537 .
- Hu , B and Yin , HM . 1005 . Semi-linear parabolic equations with prescribed energy . Rend. Circ. Mat. Palermo , 44 : 479 – 505 .
- Jazar , M and Kiwan , R . 2008 . Blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions . Ann. Inst. H. Poincaré Anal. Non Linéaire , 25 : 215 – 218 .
- Pao , CV . 1992 . Blowing-up of solution for a nonlocal reaction-diffusion problem in combustion theory . J. Math. Anal. Appl. , 162 ( 2 ) : 591 – 600 .
- El Soufi , A , Jazar , M and Monneau , R . 2007 . A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions . Ann. Inst. H. Poincaré Anal. Non Linéaire , 24 ( 1 ) : 17 – 39 .
- Souplet , P . 1999 . Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source . J. Differ. Equ. , 153 : 374 – 406 .
- Wang , MX and Wang , YM . 1996 . Properties of positive solutions for non-local reaction-diffusion problems . Math. Methods Appl. Sci. , 19 : 1141 – 1156 .
- Wang , MX . 2002 . Some degenerate and quasilinear parabolic systems not in divergence form . J. Math. Anal. Appl. , 274 : 424 – 436 .
- Wang , S , Wang , MX and Xie , CH . 2000 . A nonlinear degenerate diffusion equation not in divergence form . Z. Angew. Math. Phys. , 51 : 149 – 159 .
- Ladyzenskaja , OA , Solonnikov , VA and Ural'ceva , NN . 1968 . Linear and Quasilinear Equations of Parabolic Type , Providence : American Mathematical Society .
- Pao , CV . 1993 . Nonlinear Parabolic and Elliptic Equations , New York : Plenum Press .
- Anderson , JR . 1991 . Local existence and uniqueness of solutions of degenerate parabolic equations . Commun. Partial Differ. Equ. , 16 : 105 – 143 .
- Friedman , A and Mcleod , JB . 1986 . Blow up of solutions of nonlinear degenerate parabolic equations . Arch. Ration. Mech. Anal. , 96 : 55 – 80 .
- Wiegner , M . 1994 . Blow up for solutions of some degenerate parabolic equations . Differ. Integral Equ. , 7 : 1641 – 1647 .
- Friedman , A and Mcleod , JB . 1985 . Blow-up of positive solutions of semilinear heat equations . Indiana Univ. Math. J. , 34 : 425 – 447 .