An integro-PDE model with variable motility

Han, Byungjin; Yang, Yiren

doi:10.1016/j.nonrwa.2018.07.004

Cited by 21 publications

(11 citation statements)

References 26 publications

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“…Actually, although p ≥ 1 + 4/ N can yield blowup result for the classical Schrödinger equation i∂ t ψ + △ ψ + | ψ | p − 1 ψ = 0, our discussion in this paper only turns out the condensation effect can cover the Yukawa interaction as p > 3, N ≥ 2. One can also refer to other works() for similar case. The problem is we cannot point out whether this is a sharp threshold for collapse or not.…”

Section: Blowup In Finite Timementioning

confidence: 99%

Finite time blowup for Klein‐Gordon‐Schrödinger system

Shi

Zhang

Wang

et al. 2019

Math Methods in App Sciences

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We investigate the blowup solutions to the Klein‐Gordon‐Schrödinger (KGS) system with power nonlinearity in spatial dimensions RN (N ≥ 2). Relying on a Lyapunov functional, we establish a perturbed virial‐type identity and prove the existence of blowup solutions for the system with a negative energy and small mass. Moreover, we obtain a new finite‐time blowup result of solutions to KGS system in the energy space by constructing a differential inequality.

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Section: Blowup In Finite Timementioning

confidence: 99%

Finite time blowup for Klein‐Gordon‐Schrödinger system

Shi

Zhang

Wang

et al. 2019

Math Methods in App Sciences

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“…It should be emphasized that the work of Berestycki et al [3] did not require that the nonlocality is weak( that is, the nonlocal delay is small). After that, many important results about traveling wave solution and the spreading speed of equation (7) have been obtained, see [1,2,11,8,7,20,16,17,18,19,39] and the references therein. In addition, traveling wave soltuions of delayed Fisher-KPP equation was also studied deeply, see [4,11,21,30] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Traveling waves for nonlocal Lotka-Volterra competition systems

Han¹,

Wang²,

Du³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we study the traveling wave solutions of a Lotka-Volterra diffusion competition system with nonlocal terms. We prove that there exists traveling wave solutions of the system connecting equilibrium (0, 0) to some unknown positive steady state for wave speed c > c * = max 2, 2 √ dr and there is no such traveling wave solutions for c < c * , where d and r respectively corresponds to the diffusion coefficients and intrinsic rate of an competition species. Furthermore, we also demonstrate the unknown steady state just is the positive equilibrium of the system when the nonlocal delays only appears in the interspecific competition term, which implies that the nonlocal delay appearing in the interspecific competition terms does not affect the existence of traveling wave solutions. Finally, for a specific kernel function, some numerical simulations are given to show that the traveling wave solutions may connect the zero equilibrium to a periodic steady state.Here the unknown functions u(x, t), v(x, t) denote the densities of two competing species, the positive constants d 1 , d 2 are the diffusion coefficients of species u and v, the positive constants a 1 , a 2 are the inter-specific competition coefficients of species u and v, the positive constants b 1 , b 2 are the intra-specific competition coefficients of species u and v, and the positive constants r 1 , r 2 are the growth rates of species

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“…Indeed, a standard calculation shows its second order derivative J ′′ (t) in time has not definite sign, even for the system with negative energy. 15,16 In this paper, we eventually introduce a new modification…”

Section: Introductionmentioning

confidence: 99%

Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit

Shi

Wang

2019

Math Methods in App Sciences

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In this paper, we prove finite‐time blowup in energy space for the three‐dimensional Klein‐Gordon‐Zakharov (KGZ) system by modified concavity method. We obtain the blow‐up rates of solutions in local and global space, respectively. In addition, by using the energy convergence, we study the subsonic limit of the Cauchy problem for KGZ system and prove that any finite energy solution converges to the corresponding solution of Klein‐Gordon equation in energy space.

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An integro-PDE model with variable motility

Cited by 21 publications

References 26 publications

Finite time blowup for Klein‐Gordon‐Schrödinger system

Finite time blowup for Klein‐Gordon‐Schrödinger system

Traveling waves for nonlocal Lotka-Volterra competition systems

Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit

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