Project Name :
Nonlinear evolution equations. Blow-up phenomena. Stability and instability
Donor Organization :
INTAS
Budget:
35 460 EURO
Grant number :
INTAS Grant # 03-51-5007
Research Direction :
5 Mathematics, Mechanics
Sub Direction :
5-101 Differential Equations
Keyword(s) :
Nonlinear equation; blow-up phenomena; stability
Description :
A method of a priori estimates of solutions of one-sided nonlinear differential inequalities and systems of such inequalities with nonlinear and linear boundary data is developed. On the basis of this method, there are investigated: (i) boundary value problems on a finite and an infinite intervals for nonlinear ordinary differential equations and systems; (ii) initial-boundary and boundary value problems in a characteristic rectangle for higher order nonlinear hyperbolic equations; (iii) a problem on existence and estimate of blow-up solutions of nonlinear differential systems.
For second order nonlinear ordinary differential equations, the Dirichlet singular problem as well as a mixed problem are studied on a finite interval, and a problem on existence of bounded and non-oscillatory solutions are investigated on an infinite interval. For higher order nonlinear functional differential equations, a periodic problem is studied.
The local and global solvability of the characteristic Cauchy and Darboux type problems for the nonlinear Klein-Gordon and Sine-Gordon equations and wave equations with power nonlinearities are studied.
The local and global solvability of the Cauchy and Darboux type problems for second order nonlinear hyperbolic equations with parabolic degenerations are investigated.
Duration :
01/01/2004 - 31/12/2007
Project Leader :
No leader
Project manager :
Project participant(s) :
Nino Partsvania
01/01/2004 - 31/12/2007
Ivan Kiguradze
01/01/2004 - 31/12/2007
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