Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
By Yihong Du, Zhigui Lin. SIAM Journal on Mathematical Analysis, 2010
542 citations recorded by the source corpus.
Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science
View Paper: https://www.semanticscholar.org/paper/50e33b153aee0d459550616d52757aa80b65fa8d
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Citations in the corpus
- The diffusive logistic equation with a free boundary and sign-changing coefficient (2014, background): “Du & Guo [7, 8], Du, Guo & Peng [9] and Du & Liang [10] considered the higher space dimensions, heterogeneous environment and time-periodic environment case, where the heterogeneous environment coefficients were required to have positive lower and upper bounds.”
- Dynamics for a diffusive prey-predator model with different free boundaries (2015, background): “Please refer to [6]-[9], [11]-[13], [16, 21, 22, 28, 35, 37] and the references therein.”
- Regularity and Asymptotic Behavior of Nonlinear Stefan Problems (2014, unknown): “In space dimension 1, and in several space dimensions with radial symmetry, it was proved in [9] and [7] that problem (1.”
- A diffusive logistic model with a free boundary in time-periodic environment☆ (2013, background): “To determine the evolution of the front {|x| = h(t)} with time, we assume as in [12, 9] that the front invades at a speed that is proportional to the spatial gradient of the density function u there, which gives rise to the free boundary condition in (1.”
- Invasion of open space by two competitors: spreading properties of monostable two‐species competition‐diffusion systems (2018, unknown): “It is well known (see Du–Lin [5, 6]) that there exists a unique solution of⎧⎪⎨ ⎪⎩ −ϕ′′ = ϕ(1 − a− ϕ) in (0,+∞) ϕ(0) = 0 ϕ(x) > 0 for all x > 0 .”
- Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆ (2011, methodology): “In the special case of one space dimension and homogeneous environment, this free boundary problem was investigated in [10].”
- Invasion by an inferior or superior competitor: A diffusive competition model with a free boundary in a heterogeneous environment (2015, background): “which was investigated well in [8] and [6].”
- Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients (2015, methodology): “Inspired by [7, 33], we are going to construct the suitable upper solutions and apply Proposition 3.”
- On some Free Boundary Problems of the Prey-predator Model (2013, methodology): “For example, it was used to describe the melting of ice in contact with water [28], the modeling of oxygen in the muscle [5], the wound healing [3], the tumor growth [4], and the spreading of species [7, 8, 10, 11, 13, 14, 16, 17, 21, 29, 30].”
- A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment (2015, background): “For example, when a and b are positive constants, the problem (1.1) was investigated earlier by [13] for α = 0 and by [23] for β = 0; when a = a(x) and b = b(x), the problem (1.1) was discussed by Du, Guo & Liang [9, 12] for the higher dimension and radially symmetric case; the non-radial case in hi”
- Existence and uniqueness of solutions of free boundary problems in heterogeneous environments (2019, background): “In these references, proofs of the existence and uniqueness of local solutions were omitted and these authors claimed that the proofs are parallel to the cases of [4, 13] with constant coefficients.”
- Free Boundary Problems for a Lotka–Volterra Competition System (2014, methodology): “In the absence of v, the problems (NFB) and (DFB) are reduced to the one phase Stefan problems which were studied by Du and Lin in [6], Kaneko and Yamadae in [14] respectively.”