Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory

Onyido, Maria Amarakristi; Shen, Wenxian

doi:10.1016/j.jde.2021.05.050

Cited by 11 publications

(13 citation statements)

References 38 publications

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“…Combining these two directions, recently Shen and Vo [45] and Su et al [48] discussed the asymptotic behavior of the generalized principal eigenvalue with respect to the diffusion rate in the time-periodic case. There are also many other studies on the analysis of principal eigenvalues for nonlocal diffusion equations in different situations, the interested readers can refer to Liang et al [31], Smith [47], Coville and Hamel [11], De Leenheer et al [12], Onyido and Shen [38] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties

Ducrot¹,

Hao²,

Ruan³

2022

Preprint

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Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other and the age structure of individuals matters. In the first part of our series papers, we study the principal spectral theory of age-structured models with nonlocal diffusion of Dirichlet type. First, we provide two criteria on the existence of principal eigenvalues by using the theory of resolvent positive operators with their perturbations. Then we define the generalized principal eigenvalue and use it to investigate the influence of diffusion rate on the principal eigenvalue. In addition, we establish the strong maximum principle for age-structured nonlocal diffusion operators. In the second part [15] we will investigate the effects of principal eigenvalues on the global dynamics of the model with monotone nonlinearity in the birth rate and show that the principal eigenvalue being zero is critical.

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Section: Introductionmentioning

confidence: 99%

Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties

Ducrot¹,

Hao²,

Ruan³

2022

Preprint

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“…is the linearization of (1) at this trivial solution. Hence the principal spectral theory established for (12) in [23] has its own interests and also plays an important role in the study of the asymptotic dynamics of (1) in this paper.…”

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confidence: 99%

“…To state the main results on the asymptotic dynamics of strictly positive solutions of (1) and some new properties of the generalized principal eigenvalues of (12) to be established in this paper, we first recall some of the results on the principal spectrum of (12) established in [23].…”

mentioning

confidence: 99%

“…Principal spectral theory of (12). In this subsection, we recall some of the results on the principal spectrum of (12) established in [23].…”

mentioning

confidence: 99%

“…and 15) and ( 16) is needed for the comparison principle (see the proof of Proposition 4). In the definition of the sets Λ P E (a, D) and Λ P E (a, D) in [23], this condition was absent, which is not because it was not needed, but was missed.…”

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confidence: 99%

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Non-local dispersal equations with almost periodic dependence. II. Asymptotic dynamics of Fisher-KPP equations

Onyido¹,

Shen²

2023

DCDS-S

Self Cite

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<p style='text-indent:20px;'>This series of two papers is devoted to the study of the principal spectral theory of nonlocal dispersal operators with almost periodic dependence and the study of the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence. In the first part of the series, we investigated the principal spectral theory of nonlocal dispersal operators from two aspects: top Lyapunov exponents and generalized principal eigenvalues. Among others, we provided various characterizations of the top Lyapunov exponents and generalized principal eigenvalues, established the relations between them, and studied the effect of time and space variations on them. In this second part of the series, we study the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence applying the principal spectral theory developed in the first part. In particular, we study the existence, uniqueness, and stability of strictly positive almost periodic solutions of Fisher KPP equations with nonlocal dispersal and almost periodic dependence. Using the properties of the asymptotic dynamics of nonlocal dispersal Fisher-KPP equations, we also establish a new property of the generalized principal eigenvalues of nonlocal dispersal operators in this paper.</p>

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Perturbation problem for the indefinite nonlocal periodic-parabolic equation

Sun

Fan

2022

Z. Angew. Math. Phys.

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Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory

Cited by 11 publications

References 38 publications

Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties

Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties

Non-local dispersal equations with almost periodic dependence. II. Asymptotic dynamics of Fisher-KPP equations

Perturbation problem for the indefinite nonlocal periodic-parabolic equation

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