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VOLTERRA-LOTKA REKABET MODELİNİ TEMSİL EDEN DENKLEM SİSTEMİNİN GLOBAL ÇÖZÜMÜNÜN YOKLUĞU

NONEXISTENCE OF GLOBAL SOLUTION OF EQUATION SYSTEM REPRESENTING THE VOLTERRA-LOTKA COMPETITION MODEL

Journal Name:

  • Sigma Mühendislik ve Fen Bilimleri Dergisi

Publication Year:

  • 2004

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this study, the problem of nonexistence of global solution of equation system representing the VolterraLotka competition model in ecology, is handled with Neumann boundary conditions where n Ω ⊂ R is bounded and sufficiently uniform. While examining this problem, the generalized concavity method improved by V.K. Kalantarov and O.A. Ladyzhenskaya is used. In this method, under the existence of local solution, by using energy integral, it is shown that the positive ψ (t ) function, having the properties of the equation and the boundary conditions and representing the local solution of the equation under defined norm, satisfies the hypotheses of Kalantarov-Ladyzhenskaya Lemma. In conclusion, it is found that the ψ ( )t function namely the norm of the solution is infinite at a finite time t.
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Abstract (Original Language): 
Bu çalışmada; yeterince düzgün sınıra sahip bir bölgede ekolojide Volterra-Lotka rekabet modelini temsil eden denklem sisteminin global çözümünün yokluğu problemi, Neumann sınır koşulu ile ele alınmıştır. Bu problem incelenirken V.K. Kalantarov ve O.A. Ladyzhenskaya tarafından geliştirilen genelleştirilmiş konkavlık yöntemi kullanılmıştır. Bu yöntemde, yerel çözümün varlığı temel alınarak, enerji integrali yardımıyla, denklemin ve sınır koşullarının özelliklerini taşıyan ve belli bir norma göre denklemin yerel çözümünü temsil eden pozitif bir ψ(t) fonksiyonunun, Kalantarov-Ladyzhenskaya Lemmasının hipotezlerini sağladığı gösterilir. Sonuçta, ψ(t) fonksiyonunun yani çözümün normunun sonlu bir t anında sonsuz olduğu bulunur.
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  • 3
50-59
  • Turkish

REFERENCES

References: 

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[6] Kalantarov V. K. and Ladyzhenskaya O. A., “The Occurence of Collapse for Quasilinear
Equations of Parabolic and Hyperbolic type “, J.Soviet Math.10, 53-70, 1978, Translated
from Zap. Nauch. Sem. LOMI, 69, 77-102, 1977.

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