具非线性对流项扩散方程的源型解

研究主部为热传导算子的拟线性抛物型方程Cauchy问题:u_t=u_(xx) (u~n)_x,(x,t)∈S=R×(0,∞),u(x,0)=δ(x),x∈■在一维情形下源型解的存在性,唯一性,不存在性,解的渐近性和相似源型解等问题.在研究过程中,找到了一个n的临界值,即n_0=3.当0≤n相似文献   

Phase transition thresholds for some Friedman-style independence results

We classify the phase transition thresholds from provability to unprovability for certain Friedman-style miniaturizations of Kruskal's Theorem and Higman's Lemma. In addition we prove a new and unexpected phase transition result for ε₀. Motivated by renormalization and universality issues from statistical physics we finally state a universality hypothesis. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extension of the Method of Quasilinearization and Rapid Convergence

An extension of the method of quasilinearization has been applied to first-order nonlinear initial-value problems (IVP for short). It has been shown that there exist monotone sequences which converge rapidly to the unique solution of IVP.     

EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＴＨＥＥＮＴＲＯＰＹＳＯＬＵＴＩＯＮＴＯＡＮＯＮＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮ￥Ｒ．ＥＹＭＡＲＤ；Ｔ．ＧＡＬＬＯＵＥＴ；Ｒ．ＨＥＲＢＩＮ（ＬａｂｏｒａｔｏｉｒｅＣｅｎｔｒａｌｄｅｓＰｏ...     

椭圆型特征值问题正特征函数 的存在性和唯一性

本文讨论带Ｄｉｒｉｃｈｌｅｔ边值条件的非线性椭圆型特征值问题，给出了正特征函数存在和唯一的充分必要条件．     

两种群竞争系统持续生存的条件

本文研究两种群竞争系统持续存在性和全局渐近稳定性。新近文〔２〕保持了文〔１〕的条件而推广了方程，文〔３〕减弱了文〔１〕的条件。我们则改进文〔１〕的条件，但与文〔３〕中定理１的条件互不包含，且有新意。     

About contingent epiderivatives

In this paper we analyze some questions concerning the contingent epiderivative. When the ordering cone is not necessarily pointed we introduce the notion of family of contingent epiderivatives. We also investigate the relationship between the contingent derivative and the generalized epiderivative. Furthermore, we give existence theorems with respect to Daniell cones. As a particular case, we study set-valued maps that take values in Rn.     

Some existence results for a class of degenerate semilinear elliptic systems

Using a variational approach, we investigate a class of degenerate semilinear elliptic systems with measurable, unbounded nonnegative weights, where the domain is bounded or unbounded. Some existence results are obtained.     

Existence and uniqueness of local solutions to a class of quasilinear degenerate parabolic systems

In this paper, the authors study an initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use the method of regularization to construct a sequence of approximation solutions with the help of monotone iteration technique and hence obtain the existence of solutions to a regularized system of equations. Then the existence of solutions to the system of evolution p-Laplacian equations is obtained with the use of a standard limiting process. The uniqueness of the solution is also proven.