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1.
Liang Zhao 《Journal of Differential Equations》2019,266(9):5615-5624
In this paper, let be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation where are real constants. 相似文献
2.
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
3.
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5.
Andrea Blunck 《Monatshefte für Mathematik》1997,123(2):93-107
In this note we show that the chain space belonging to a quadric can be embedded into the chain geometry over a Clifford algebra via a generalized stereographic projection. 相似文献
6.
Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung 相似文献
7.
Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation. 相似文献
8.
9.
For z1,z2,z3∈Zn, the tristance d3(z1,z2,z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticodeAd of diameter d is a subset of Zn with the property that d3(z1,z2,z3)?d for all z1,z2,z3∈Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z2 for all diameters d?1. We then generalize this result to two related distance models: a different distance structure on Z2 where d(z1,z2)=1 if z1,z2 are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z2 is replaced by the hexagonal lattice A2. We also investigate optimal tristance anticodes in Z3 and optimal quadristance anticodes in Z2, and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multi-dimensional interleaving schemes and to connectivity loci in the game of Go. 相似文献
10.
M. Brokate D. Rachinskii 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):385-411
The paper is concerned with the study of plasticity models described by differential equations with stop and play operators.
We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the
vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another
class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions.
The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research
fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged. 相似文献