caa a22 4500 477075576 CHVBK 20180405111438.0 cr unu---uuuuu 170330e19960601xx s 000 0 eng 10.1007/BF02901223 doi (NATIONALLICENCE)springer-10.1007/BF02901223 Initial-boundary value problem for a class of quasilinear degenerate parabolic equations [Elektronische Daten] [Nie Lei, Xu Chaojiang] In this work, we study the quasilinear initial-boundary value problem $$\sum\limits_{i, j = 1}^m {X_i^ * A_{i j} (x, t, u)X _j u} + \sum\limits_{j = 1}^m {B_j (x, t, u)X _j u + C} (x, t, u) = 0$$ , in ]0,T[×Ω;u| t=0 =φ, onΩ;u=ψ, on [0,T[×∂Ω, whereX={X 1, ...,X m } is a system of real smooth vector fields which is defined on an open domainM of R n , and satisfies the Hörmander's condition, Ω⊂M. Assume that ∂Ω is non characteristic for the systemX 1,...,X m . Under some hypothesis for the boundary of domain and the elliptic structure condition for nonlinear coefficientsA ij ,B j ,C, (i, j=1, ...,m), we have proved that the existence and regularity of solution for aboveinitial-boudary value problems. Springer, 1996 degenerate parabolic equation nationallicence vector fields nationallicence non-isotropic Hölder's space nationallicence initial-boundary value problem nationallicence Lei Nie Institute of Mathematics, Wuhan University, 430072, Wuhan, China aut Chaojiang Xu Institute of Mathematics, Wuhan University, 430072, Wuhan, China aut Wuhan University Journal of Natural Sciences Wuhan University 1/2(1996-06-01), 179-183 1007-1202 1:2<179 1996 1 11859 https://doi.org/10.1007/BF02901223 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02901223 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lei Nie Institute of Mathematics, Wuhan University, 430072, Wuhan, China aut NATIONALLICENCE 700 1- Chaojiang Xu Institute of Mathematics, Wuhan University, 430072, Wuhan, China aut NATIONALLICENCE 773 0- Wuhan University Journal of Natural Sciences Wuhan University 1/2(1996-06-01), 179-183 1007-1202 1:2<179 1996 1 11859 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer