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31.
This paper is concerned with the traveling waves of a reaction-diffusion SIRQ epidemic model with relapse. We find that the existence and nonexistence of traveling waves are determined by the basic reproduction number of the system and the minimal wave speed. This threshold dynamics is proved by Schauder''s fixed-point theorem combining Lyapunov functional with the theory of asymptotic spreading. Moreover, the numerical simulations are provided to illustrate our analytical results and the effect of the relapse is also discussed.  相似文献   
32.
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN. The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.  相似文献   
33.
ABSTRACT

Results appearing in this paper can be used to establish the solvability of nonlinear discrete time systems subject to generalized nonlinear boundary conditions. Two separate sets of results are established, each of which can be used to establish existence of solutions to problems for which previous related work proves inconclusive. The first set of results imposes conditions on the sizes of nonlinearities, while the second framework requires geometric properties of the nonlinearity in the dynamics.  相似文献   
34.
Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of n reaction–diffusion–convection equations coupled with n ordinary differential equations, which models a combustion front moving through a porous medium with n parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.  相似文献   
35.
We consider nonlinear partial differential equations with several Fuchsian variables of type , where is a Fuchsian principal part of weight zero. We prove existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the Fuchsian variable and in Gevrey spaces with respect to the other variable . The method of proof is based on the application of the fixed point theorem in some Banach algebras defined by majorant functions that are suitable to this kind of equation.

  相似文献   

36.
When the matrices $A$ and $Q$ have special structure, the structure-preserving algorithm was used to compute the stabilizing solution of the complex matrix equation $X+A^TX^{-1}A=Q.$ In this paper, we study the numerical methods to solve the complex symmetric stabilizing solution of the general matrix equation $X+A^TX^{-1}A=Q.$ We not only establish the global convergence for the methods under an assumption, but also show the feasibility and effectiveness of them by numerical experiments.  相似文献   
37.
In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. By applying the Schauder's fixed-point theorem, we prove that the It improves the result of 0 ≤ Q 〈 1 in problem admits a solution for 0 ≤ Q ≤ 14.306 [2] and 0 ≤ Q ≤ 13.213 in [3].  相似文献   
38.
39.
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative Dαo+is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.  相似文献   
40.
The Scheinkman-Weiss model and later works by Conze-Lasry-Scheinkman provide insights on cycles and correlations of economies with incomplete markets, namely with borrowing constraints. This work gives a mathematical solution in the case of high relative risk aversion, which has not yet been solved. The existence of an equilibrium results from the solution of a system of nonlinear functional differential equations. High risk aversion leads to new mathematical difficulties, not present in previous papers on this subject.This work is an extension of previous works done under the direction of Professor Jean-Michel Lasry, University of Paris 9, Dauphine. The author is sincerely grateful to Professor Lasry who suggested the idea of this article and whose remarks were always of help.  相似文献   
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