2020
DOI: 10.1016/j.na.2020.111836
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Front blocking versus propagation in the presence of drift term varying in the direction of propagation

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Cited by 9 publications
(11 citation statements)
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“…(1.16) However, under some other geometrical conditions (when typically, the cross section is narrow and then becomes abruptly much wider), blocking phenomena can occur, in the sense of (1.15). Further propagation and/or blocking phenomena were also shown for bistable equations set in the real line R (with periodic heterogeneities [12,13,16,29,[39][40][41], with local defects [9,10,32,33,35,37], or with asymptotically distinct left and right environments [18]), as well as in straight infinite cylinders with non-constant drifts [19,20], and in some periodic domains [14] or the whole space with periodic coefficients [15,23]. In [36], a reaction-diffusion model was considered to analyse the effects on population persistence of simultaneous changes in the position and shape of a climate envelope.…”
Section: Introductionmentioning
confidence: 78%
“…(1.16) However, under some other geometrical conditions (when typically, the cross section is narrow and then becomes abruptly much wider), blocking phenomena can occur, in the sense of (1.15). Further propagation and/or blocking phenomena were also shown for bistable equations set in the real line R (with periodic heterogeneities [12,13,16,29,[39][40][41], with local defects [9,10,32,33,35,37], or with asymptotically distinct left and right environments [18]), as well as in straight infinite cylinders with non-constant drifts [19,20], and in some periodic domains [14] or the whole space with periodic coefficients [15,23]. In [36], a reaction-diffusion model was considered to analyse the effects on population persistence of simultaneous changes in the position and shape of a climate envelope.…”
Section: Introductionmentioning
confidence: 78%
“…Remark 1.3. An analogous criterion for almost unchanged propagation as in the one-dimensional case in [7] does also hold in the n-dimensional case, ie. Theorem 1.4 (almost unchanged propagation).…”
Section: Introductionmentioning
confidence: 84%
“…Remark 1.5. For n = 1 even though we did only derive the criterion for n ≥ 3 the expression behaves as in [7]. But due to the Sobolev-embeddings becoming weaker in increasing dimensions, this generalized criterion is weaker, in the sense that the criterion for n > m might not be satisfied for an m-dimensional drift term constantly extended to n dimensions, that satisfies the criterion in m dimensions.…”
Section: Introductionmentioning
confidence: 96%
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