Nonlinearly determined wavefronts of the Nicholson's diffusive equation: when small delays are not ...

@article{39682,
   author = {Hasík, Karel and Kopfová, Jana and Nábělková, Petra and Trofimchuk, Sergei and Chladná, Zuzana},
   article_location = {San DIego},
   article_number = {9},
   doi = {http://dx.doi.org/10.1016/j.jde.2019.11.007},
   keywords = {Non-linear determinacy; Delay; Wavefront; Existence; Super-exponential solution},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Nonlinearly determined wavefronts of the Nicholson's diffusive equation: when small delays are not harmless},
   url = {https://www.sciencedirect.com/science/article/pii/S0022039619305352?via%3Dihub},
   volume = {268},
   year = {2020}
}

TY  - JOUR
ID  - 39682
AU  - Hasík, Karel - Kopfová, Jana - Nábělková, Petra - Trofimchuk, Sergei - Chladná, Zuzana
PY  - 2020
TI  - Nonlinearly determined wavefronts of the Nicholson's diffusive equation: when small delays are not harmless
JF  - Journal of Differential Equations
VL  - 268
IS  - 9
SP  - 5156-5178
EP  - 5156-5178
PB  - Academic Press Inc. Elsevier Science
SN  - 00220396
KW  - Non-linear determinacy
KW  - Delay
KW  - Wavefront
KW  - Existence
KW  - Super-exponential solution
UR  - https://www.sciencedirect.com/science/article/pii/S0022039619305352?via%3Dihub
L2  - https://www.sciencedirect.com/science/article/pii/S0022039619305352?via%3Dihub
N2  - By proving the existence of non-monotone and non-oscillating wavefronts for the Nicholson's blowflies diffusive equation (the NDE), we answer an open question from [16]. Surprisingly, wavefronts of such a kind can be observed even for arbitrarily small delays. Similarly to the pushed fronts, obtained waves are not linearly determined. In contrast, a broader family of eventually monotone wavefronts for the NDE is indeed determined by properties of the spectra of the linearized equations. Our proofs use essentially several specific characteristics of the blowflies birth function (its unimodal form and the negativity of its Schwarz derivative, among others). One of the key auxiliary results of the paper shows that the Mallet-Paret-Cao-Arino theory of super-exponential solutions for scalar equations can be extended for some classes of second order delay differential equations. For the new type of non-monotone waves to the NDE, our numerical simulations also confirm their stability properties established by Mei et al.
ER  - 

HASÍK, Karel, Jana KOPFOVÁ, Petra NÁBĚLKOVÁ, Sergei TROFIMCHUK a Zuzana CHLADNÁ. Nonlinearly determined wavefronts of the Nicholson's diffusive equation: when small delays are not harmless. \textit{Journal of Differential Equations}. San DIego: Academic Press Inc. Elsevier Science, 2020, roč.~268, č.~9, s.~5156-5178. ISSN~0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2019.11.007.