Další formáty:
BibTeX
LaTeX
RIS
@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.
|