| EXISTENCE AND UNIQUENESS OFWEAK SOLUTIONS OF UNIFORMLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS |
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| 引用本文： | Chen Yazhe. EXISTENCE AND UNIQUENESS OFWEAK SOLUTIONS OF UNIFORMLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS[J]. 数学年刊B辑(英文版), 1985, 6(2): 131-146 |
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| 作者姓名： | Chen Yazhe |
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| 作者单位： | Department of |
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| 摘 要： | In this paper we deal with the quasilinear parabolic equation u/t=/x_i[a_(ij)(x, t, u))u/x_j]+b_i(x, t, u)u/x_i+c(x, t, u) which is uniformly degenerate at u=O. Under some assumptions we prove existence anduniqueness of nonnegative weak solutions to the Cauchy problem and the first boundary valueproblem for this equation. Furthermore, the weak solutions are globally Holder continuous.
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| 收稿时间： | 1982-10-04 |
Existence and Uniqueness of Weak Solutions of Uniformly Degenerate Quasilinear Parabolic Equations |
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| Chen Yazhe. Existence and Uniqueness of Weak Solutions of Uniformly Degenerate Quasilinear Parabolic Equations[J]. Chinese Annals of Mathematics,Series B, 1985, 6(2): 131-146 |
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| Authors: | Chen Yazhe |
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| Affiliation: | Department of Mathematics, Beijing University, Beijing, China. |
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| Abstract: | In this paper we deal with the quasilinear parabolic equation$[frac{{partial u}}{{partial t}} = frac{partial }{{partial {x_i}}}[{a_{ij}}(x,t,u)frac{{partial u}}{{partial {x_j}}}] + {b_i}(x,t,u)frac{{partial u}}{{partial {x_i}}} + c(x,t,u)]$which is uniformly degenerate at u=0. Under some assumptions we prove existence and uniqueness of nonnegative weak solutions to the Cauchy problem and the first boundary value problem for this equation. Furthermore, the weak solutions are globally Holder continuous. |
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