共查询到18条相似文献,搜索用时 328 毫秒
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研究了一类趋化性生物模型行波解的存在性和正则性.通过直接计算得到了其行波解存在的充分必要条件;在一定条件下,研究了行波解的正则与非正则的性质;在特殊情形下给出了行波解的显式解. 相似文献
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杨瑜 《数学物理学报(A辑)》2022,(5):1409-1415
该文考虑了一类非局部扩散的SIR模型.首先,当R0> 1,c=c*时,研究模型的临界行波解的存在性.最后,当R0<1时,讨论模型的行波解的不存在性.完善了已有文献的一些结果. 相似文献
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针对部分种群个体活动而其他个体静止的单种群模型,主要研究了一维格上具有静止阶段的时滞反应扩散系统的行波解的定性性质.在单稳和拟单调的假设条件下,首先,研究了行波解的存在性.其次,证明了行波解的渐近行为、单调性以及唯一性.最后,证明了所有非临界波前解(即波速大于最小波速的波前解)是指数渐近稳定的. 相似文献
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讨论了一类带有扩散与时滞的流行性传染病模型的行波解的存在性.首先,将系统的行波解的存在性问题转化为一个二阶常微分方程组的单调解的存在性问题;应用单调方法和不动点方法,进一步地将问题转化为方程组的上下解的构造问题;应用所建立的引理与定理,通过构造适合的上下解,证明了系统单调行波解的存在性. 相似文献
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针对种群中的染病个体在疾病潜伏期内具有自由移动和传染疾病的现象,研究了一个具有时空时滞的非局部扩散SIR模型的行波解问题.利用基本再生数和最小波速判定行波解是否存在.首先,通过在有界区域上构造一个初始函数的不变锥,利用Schauder不动点定理证明在该锥上存在不动点,然后通过取极限的方法得到行波解的存在性.其次,利用双边Laplace(拉普拉斯)变换法证明了行波解的不存在性.由于行波解的最小传播速度对控制疾病传播具有重要的指导意义,最后讨论了非局部扩散、时滞等因素对最小波速的影响. 相似文献
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This paper deals with the existence of traveling wave solutions of a class of delayed system of lattice differential equations, which formulates the invasion process when two competitive species are invaders. Employing the comparison principle of competitive systems, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. More precisely, by the cross-iteration, the existence of traveling wave solutions is reduced to the existence of an admissible pair of upper and lower solutions. To illustrate our main results, we prove the existence of traveling wave solutions in two delayed two-species competition systems with spatial discretization. Our results imply that the delay appeared in the interspecific competition terms do not affect the existence of traveling wave solutions. 相似文献
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Shuxia Pan 《Nonlinear Analysis: Real World Applications》2009,10(5):2807-2818
This paper is concerned with the existence of traveling wave solutions for delayed reaction diffusion systems which contain the competition diffusion systems with time lags. By using a cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of admissible upper and lower solutions, which also provides a constructive process of the traveling wave solutions. To illustrate our conclusion, we consider a delayed diffusion system with the Gilpin–Ayala type nonlinearity and establish the existence of its traveling wave solutions, which cannot be answered by the existing results. 相似文献
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Wenzhang Huang 《Journal of Mathematical Analysis and Applications》2006,316(1):42-59
The existence of traveling wave solutions for a reaction-diffusion, which serves as models for microbial growth in a flow reactor and for mathematical epidemiology, was previously confirmed. However, the problem on the uniqueness of traveling wave solutions remains open. In this paper we give a complete proof of the uniqueness of traveling wave solutions. 相似文献
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Approximate damped oscillatory solutions for compound KdV-Burgers equation and their error estimates
In this paper,we focus on studying approximate solutions of damped oscillatory solutions of the compound KdV-Burgers equation and their error estimates.We employ the theory of planar dynamical systems to study traveling wave solutions of the compound KdV-Burgers equation.We obtain some global phase portraits under different parameter conditions as well as the existence of bounded traveling wave solutions.Furthermore,we investigate the relations between the behavior of bounded traveling wave solutions and the dissipation coefficient r of the equation.We obtain two critical values of r,and find that a bounded traveling wave appears as a kink profile solitary wave if |r| is greater than or equal to some critical value,while it appears as a damped oscillatory wave if |r| is less than some critical value.By means of analysis and the undetermined coefficients method,we find that the compound KdV-Burgers equation only has three kinds of bell profile solitary wave solutions without dissipation.Based on the above discussions and according to the evolution relations of orbits in the global phase portraits,we obtain all approximate damped oscillatory solutions by using the undetermined coefficients method.Finally,using the homogenization principle,we establish the integral equations reflecting the relations between exact solutions and approximate solutions of damped oscillatory solutions.Moreover,we also give the error estimates for these approximate solutions. 相似文献
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This article studies the existence of traveling wave solutions in
an integrodifference equation with weak compactness. Because of the special
kernel function that may depend on the Dirac function, traveling wave maps
have lower regularity such that it is difficult to directly look for a traveling wave
solution in the uniformly continuous and bounded functional space. In this
paper, by introducing a proper set of potential wave profiles, we can obtain
the existence and precise asymptotic behavior of nontrivial traveling wave
solutions, during which we do not require the monotonicity of this model. 相似文献
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In this paper, we first reduce the existence of traveling wave solutions in a delayed lattice competition-cooperation system to the existence of a pair of upper and lower solutions by means of Schauder’s fixed point theorem and the cross iteration scheme, and then we construct a pair of upper and lower solutions to obtain the existence and nonexistence of traveling wave solutions. We also consider the asymptotic behaviour of any nonnegative traveling wave solutions at negative infinity. 相似文献
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This paper is concerned with the traveling wave solutions in a diffusive system with two preys and one predator. By constructing upper and lower solutions, the existence of nontrivial traveling wave solutions is established. The asymptotic behavior of traveling wave solutions is also confirmed by combining the asymptotic spreading with the contracting rectangles. Applying the theory of asymptotic spreading, the nonexistence of traveling wave solutions is proved. 相似文献