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51.
Mourad Kainane Mezadek Mohamed Kainane Mezadek Michael Reissig 《Mathematical Methods in the Applied Sciences》2020,43(6):3117-3147
In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity. 相似文献
52.
Yazid Gouari Zoubir Dahmani Mehmet Zeki Sarikaya 《Mathematical Methods in the Applied Sciences》2020,43(11):6938-6949
In this paper, using Riemann–Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane–Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results. 相似文献
53.
Tadahisa Funaki Yueyuan Gao Danielle Hilhorst 《Mathematical Methods in the Applied Sciences》2020,43(9):5860-5886
In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a -Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution. 相似文献
54.
In this paper, we consider the Cauchy problem for the three dimensional chemotaxis-Navier–Stokes equations. By exploring the new a priori estimates, we prove the global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations. 相似文献
55.
Piotr Kacprzyk 《Mathematical Methods in the Applied Sciences》2013,36(3):313-322
Global existence of regular solutions to the Navier–Stokes equations coupled with the heat convection in a cylindrical pipe has already been shown. In this paper, we prove the existence of the global attractor to the equations and convergence of their solutions to a stationary one. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
56.
Hanwen Ning 《Applicable analysis》2013,92(4):563-577
In this article, we consider dynamic behaviours of a class of non-linear delay stochastic evolution equations. Local existence and uniqueness of the solutions are obtained with the aid of proper iterative scheme and moment estimations. We also propose a continuation result and our results generalize the known results. 相似文献
57.
58.
The aim of this paper is to study the existence and the asymptotic behavior of solutions for some reaction–diffusion equations arising in epidemic biology phenomena. We will show that for a rather broad class of nonlinearities, the solutions are global and uniformly bounded, and under suitable assumptions on the parameters of the system, these solutions converge as time goes to infinity to a disease‐free equilibrium point. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
59.
Kang Qun Zhang 《数学学报(英文版)》2012,28(6):1135-1154
In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity. 相似文献
60.
Consider K ≥ 2 independent copies of the random walk on the symmetric group SN starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let Gn be the subgroup of SN generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of Gn and for the transitivity of Gn, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of Gn appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012 相似文献