| 一类退化-奇异抛物型方程的行波解Ⅰ |
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| 引用本文： | 王明新.一类退化-奇异抛物型方程的行波解Ⅰ[J].系统科学与数学,1992,12(2):127-135. |
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| 作者姓名： | 王明新 |
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| 作者单位： | 河南大学数学系 开封475001 |
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| 摘 要： | 多孔介质动力学方程吸引了众多人的注意,引起了数学家们的极大兴趣.退化-奇异抛物型方程的行波解也成为令人瞩目的问题.Aronson,Hosono,Atkinson,Engler,Grindron 和 Sleeman,Wang 和 Ye 等在这一领域中都有出色的工作.Aronson 对 m=k=1,u~nf(u)∈C~10,1],讨论了单调行波解的存在性.Hosono 对m=1,k≥2,n=0,f∈C~20,1],f′(0)<0,f″(0)(?)0,f′(1)<0,且存在α∈
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TRAVELLING WAVE SOLUTIONS FOR SOME DEGENERATESINGULAR PARABOLIC EQUATIONS I |
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| WANG MING-XIN.TRAVELLING WAVE SOLUTIONS FOR SOME DEGENERATESINGULAR PARABOLIC EQUATIONS I[J].Journal of Systems Science and Mathematical Sciences,1992,12(2):127-135. |
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| Authors: | WANG MING-XIN |
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| Institution: | Department of Mathematics,Henan' University,Kaifeng 475001 |
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| Abstract: | The existence and regularity of travelling wave front solutions are discussed for somedegenerate-singular parabolic equations (u~m/m)_t=u_(xx)+u'f(u).It is proved that theconclusions on wave fronts for the equation u_t=u_(xx)+f(u) also hold for these degenerate-singular equations.Here f(u) is assumed to be continuous. |
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