Proceedings of the Royal Society of Edinburgh Section A: Mathematics
SCIE-ISI SCOPUS (1975-2023)
1473-7124
0308-2105
Anh Quốc
Cơ quản chủ quản: Cambridge University Press , CAMBRIDGE UNIV PRESS
Lĩnh vực:
Mathematics (miscellaneous)
Các bài báo tiêu biểu
Local existence and blow-up criterion for the Boussinesq equationsSynopsis In this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove glo... ...
Tập 127 Số 5 - Trang 935-946 - 1997
Using Melnikov's method to solve Silnikov's problemsSynopsis A function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's ... ...
Tập 116 Số 3-4 - Trang 295-325 - 1990
Permanence in ecological systems with spatial heterogeneitySynopsis A basic problem in population dynamics is that of finding criteria for the long-term coexistence of interacting species. An important aspect of the problem is determining how coexistence is affected by spatial dispersal and environmental heterogeneity. The object of this paper is to study the problem of coexistence for two interacting species dispersing thr... ...
Tập 123 Số 3 - Trang 533-559 - 1993
The bond-based peridynamic system with Dirichlet-type volume constraintIn this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is b... ...
Tập 144 Số 1 - Trang 161-186 - 2014
3.—A Criterion for the Existence of Solutions of Non-linear Elliptic Boundary Value ProblemsSynopsis By a new method it is proved that a non-linear elliptic boundary value problem of rather general type admits a weak solution lying between a given weak lower solution ϕ and a given weak upper solution ψ≧ϕ
Tập 74 - Trang 49-54 - 1976
Qualitative behaviour of positive solutions of a predator—prey model: effects of saturationWe study a predator–prey system with Holling–Tanner interaction terms. We show that if the saturation rate m is large, spatially inhomogeneous steady-state solutions arise, contrasting sharply with the small-m case, where no such solution could exist. Furthermore, for large m , we give sharp estimates on the ra... ...
Tập 131 Số 2 - Trang 321-349 - 2001
A relationship between the periodic and the Dirichlet BVPs of singular differential equationsIn this paper, a relationship between the periodic and the Dirichlet boundary value problems for second-order ordinary differential equations with singularities is established. This relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations. Using this relationship, we give in this paper an existence result of positiv... ...
Tập 128 Số 5 - Trang 1099-1114 - 1998
Practical persistence in ecological models via comparison methodsA basic question in mathematical ecology is that of deciding whether or not a model for the population dynamics of interacting species predicts their long-term coexistence. A sufficient condition for coexistence is the presence of a globally attracting positive equilibrium, but that condition may be too strong since it excludes other possibilities such as stable periodic solutions. Even if... ...
Tập 126 Số 2 - Trang 247-272 - 1996
1.—Perturbation Theory for Sobolev SpacesSynopsis This paper studies Sobolev spaces under perturbation of domains of definition. It establishes the basic concepts, methods and results for the convergence of sequences of sets in ℝn , the strong and weak convergence of sequences of Sobolev spaces, the discrete compactness of natural embeddings and the continuous convergence of continuous ... ...
Tập 73 - Trang 5-49 - 1975