Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d）...Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.展开更多
In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an ele...In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).展开更多
In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary...In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations and obstacje problems are given.展开更多
基金Supported by the Natural Science Foundation of China (10971251)
文摘Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.
文摘In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).
文摘In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations and obstacje problems are given.
