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1.
This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity. 相似文献
2.
In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
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Tsuguo SUNAMURA 《Proceedings of the Japan Academy. Series B, Physical and biological sciences》2015,91(9):481-500
Substantial progress in research on the recession of coastal cliffs composed of soft materials has been made in recent years and data with higher accuracy have been accumulated. This paper provides the state of the art review in the recession studies and highlights two new findings obtained from the reanalysis of existing data. The review topics are: episodic and localized nature of cliff recession; the development of cliffline; the relationship between cliff height and recession rate; mechanisms of cliff toe erosion by waves; a fundamental equation for wave-induced toe erosion; factors controlling toe erosion; and slope instabilities and mass movements. The findings are presented on (1) the temporal change in cliffline recession mode and (2) the effect of beach sediment at the cliff base on the cliff erosion. 相似文献
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Bobby Wilson 《偏微分方程通讯》2015,40(8):1521-1542
This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case. 相似文献
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The zero dissipation limit of the one-dimensional non-isentropic micropolar equations is studied in this paper. If the given rarefaction wave which connects to vacuum at one side, a sequence of solution to the micropolar equations can be constructed which converge to the above rarefaction wave with vacuum as the viscosity and the heat conduction coefficient tend to zero. Moreover, the uniform convergence rate is obtained. The key point in our analysis is how to control the degeneracies in the vacuum region in the zero dissipation limit process. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(2):417-456
We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold. 相似文献