The heat equation with generalized Wentzell boundary condition

被引:166
作者
Favini, A
Goldstein, GR
Goldstein, JA
Romanelli, S
机构
[1] Univ Bologna, Dipartmento Matemat, I-40126 Bologna, Italy
[2] Univ Memphis, CERI, Memphis, TN 38152 USA
[3] Memphis State Univ, Dept Math Sci, Memphis, TN 38152 USA
[4] Univ Bari, Dipartimento Interuniv Matemat, I-70125 Bari, Italy
关键词
D O I
10.1007/s00028-002-8077-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let Omega be a bounded subset of R-N, a is an element of C-1 ((Omega) over bar) with a > 0 in Omega and A be the operator defined by Au := del.(adelu) with the generalized Wentzell boundary condition Au + beta partial derivativeu/partial derivativen + yu = 0 on partial derivativeOmega If partial derivativeOmega is in C-2, beta and gamma are nonnegative functions in C-1 (partial derivativeOmega), with beta > 0, and Gamma := {x is an element of partial derivativeOmega: a(x) > 0} not equal 0, then we prove the existence of a (C-0) contraction semigroup generated by (A) over bar, the closure of A, on a suitable L-P space, 1 less than or equal to p < infinity and on C(<(Omega)over bar>). Moreover, this semigroup is analytic if 1 < p < infinity.
引用
收藏
页码:1 / 19
页数:19
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