具局部化源弱耦合退化抛物系统解的爆破性质
摘要
主要研究带有局部化源的弱耦合奇异退化抛物型方程组解的整体存在性和爆破性质,并给出了同时爆破的充分条件及必要条件;最后在系统爆破的前提下,得出一致爆破模式。
引文
[1]J.M.Chadam,A.Peirce,H.M.Yin.The blow up property of solutions to some diffusion equations with localized nonlinear reactions[J].J.Math.Anal.Appl.,1992.
[2]P.Souplet.Uniform blow-up profiles and boundary behavior for diffusion equations with non-local nonlinear source[J].J.Diff.Equations,1999.
[3]M.X.Wang.Blow-up rate estimates for semi linear parabolic system[J].J.of Diff.Equs.,2001(170).
[4]刘其林,李玉祥,高洪俊.非局部反应扩散方程组的爆破性质[J].数学学报,2006(49).
[5]H.L.Li,M.X.Wang.Uniform blowup profiles and boundary layer for a parabolic system with localized nonlinear reaction terms[J].Sci.China Ser.A Math.,2005(48).
[6]Xiang,Z.Y.,Hu,X.G.,Mu,C.L.:Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources[J].Non-linear Anal.,2005(61).
[7]Zhou,J.,Mu,C.L.:Global existence and blow-up for weakly coupled degenerate and singular parabolic equations with localized source[J].Z.Angew.Math.Phys.2011(62).
[2]P.Souplet.Uniform blow-up profiles and boundary behavior for diffusion equations with non-local nonlinear source[J].J.Diff.Equations,1999.
[3]M.X.Wang.Blow-up rate estimates for semi linear parabolic system[J].J.of Diff.Equs.,2001(170).
[4]刘其林,李玉祥,高洪俊.非局部反应扩散方程组的爆破性质[J].数学学报,2006(49).
[5]H.L.Li,M.X.Wang.Uniform blowup profiles and boundary layer for a parabolic system with localized nonlinear reaction terms[J].Sci.China Ser.A Math.,2005(48).
[6]Xiang,Z.Y.,Hu,X.G.,Mu,C.L.:Neumann problem for reaction-diffusion systems with nonlocal nonlinear sources[J].Non-linear Anal.,2005(61).
[7]Zhou,J.,Mu,C.L.:Global existence and blow-up for weakly coupled degenerate and singular parabolic equations with localized source[J].Z.Angew.Math.Phys.2011(62).