Destabilization for quasivariational inequalities of reaction-diffusion type

Vítězslav Babický

Applications of Mathematics (2000)

  • Volume: 45, Issue: 3, page 161-176
  • ISSN: 0862-7940

Abstract

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We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.

How to cite

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Babický, Vítězslav. "Destabilization for quasivariational inequalities of reaction-diffusion type." Applications of Mathematics 45.3 (2000): 161-176. <http://eudml.org/doc/33054>.

@article{Babický2000,
abstract = {We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.},
author = {Babický, Vítězslav},
journal = {Applications of Mathematics},
keywords = {reaction-diffusion system; unilateral conditions; quasivariational inequality; Leray-Schauder degree; eigenvalue; stability; reaction-diffusion system; unilateral boundary condition; quasivariational inequality; Leray-Schauder degree; eigenvalue},
language = {eng},
number = {3},
pages = {161-176},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Destabilization for quasivariational inequalities of reaction-diffusion type},
url = {http://eudml.org/doc/33054},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Babický, Vítězslav
TI - Destabilization for quasivariational inequalities of reaction-diffusion type
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 3
SP - 161
EP - 176
AB - We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
LA - eng
KW - reaction-diffusion system; unilateral conditions; quasivariational inequality; Leray-Schauder degree; eigenvalue; stability; reaction-diffusion system; unilateral boundary condition; quasivariational inequality; Leray-Schauder degree; eigenvalue
UR - http://eudml.org/doc/33054
ER -

References

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