Monostable waves in a class of non-local convolution differential equation

Xu, Zhaoquan; Wu, Chufen

doi:10.1016/j.jmaa.2018.02.036

Cited by 3 publications

(3 citation statements)

References 40 publications

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“…For example, we prove that the upward convergence of spreading speed by using fluctuation method. These results together with the wave propagation results established in our recent work [32] also lead to the conclusion that the spreading speed of (5) coincides with the minimal wave speed of traveling waves in the general case.…”

supporting

confidence: 82%

Spreading speeds for a class of non-local convolution differential equation

Xu¹,

Wu²

2020

DCDS-B

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supporting

confidence: 82%

Spreading speeds for a class of non-local convolution differential equation

Xu¹,

Wu²

2020

DCDS-B

Self Cite

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“…Various convolution-type equations have been studied in a number of settings. For example, Schumacher [34] and Xu and Wu [38] studied wave propagation dynamics in the case of convolution-type equations; the qualitative properties of such solutions was studied. Similarly, Diekmann and Kaper [11] analyzed the existence and uniqueness of solution to nonlinear convolution equations similar to (1).…”

Section: Christopher Goodrich and Carlos Lizamamentioning

confidence: 99%

“…Suppose that ∆ α u (n) ≥ 0, (39) for each n ∈ N 0 . Then due to (38) Finally, we consider the following application to a fractional difference equation.…”

Section: Christopher Goodrich and Carlos Lizamamentioning

confidence: 99%

Positivity, monotonicity, and convexity for convolution operators

Goodrich¹,

Lizama²

2020

Discrete &Amp; Continuous Dynamical Systems - A

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We consider the convolution inequality a * u≥v for given functions a and v, and we then investigate conditions on a and v that force the unknown function u to be positive or monotone or convex. We demonstrate that these results for abstract convolution equations can be specialized to yield new insights into the qualitative properties of fractional difference and differential operators. Finally, we apply our results to finite difference methods for fractional differential equations, and we show that our results yield insights into the qualitative behavior of these types of numerical approximations.1. Introduction. The division problem is the following: Let a and v be functions defined on a time scale T ⊂ R. Can we find a function u which satisfiesThis problem was posed and solved in complete generality by B. Malgrange and L. Ehrenpreis in the fifties and sixties. However, more precise questions, e.g., the regularity of the function u, were left open. This was called the Problem B by Ehrenpreis [14]. In this paper, we address following form of the Problem B : Under which conditions on a and, eventually, on initial values of u, can we find a positive, monotone or convex function u satisfying (1) -more precisely, we replace (1) with the somewhat more general convolution inequality a * u ≥ v? As we will explain momentarily, it turns out that this question has many applications in the theory of fractional differential and difference operators as well as finite difference methods for fractional differential equations.Convolution is a widely used technique in mathematical analysis, statistics and approximation theory, and has many applications, e.g., image and signal processing.

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Spreading speed for a nonlocal diffusive delayed model without quasi-monotonicity

Liu

Weng

2020

Journal of Mathematical Analysis and Applications

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Monostable waves in a class of non-local convolution differential equation

Cited by 3 publications

References 40 publications

Spreading speeds for a class of non-local convolution differential equation

Spreading speeds for a class of non-local convolution differential equation

Positivity, monotonicity, and convexity for convolution operators

Spreading speed for a nonlocal diffusive delayed model without quasi-monotonicity

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