Exact Controllability of Nonlinear Diffusion Equations Arising in Reactor Dynamics
نویسنده
چکیده
This paper studies the problems of local exact controllability of nonlinear and global exact null controllability of linear parabolic integro-differential equations respectively with mixed and Neumann boundary data with distributed controls acting on a subdomain ω of Ω ⊂ R. The proof of the linear problem relies on a Carleman-type estimate and observability inequality for the adjoint equations and that the nonlinear one, on the fixed point technique.
منابع مشابه
Null controllability of a nonlinear diffusion system in reactor dynamics
In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of R with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a...
متن کاملExact Solution for Nonlinear Local Fractional Partial Differential Equations
In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...
متن کاملNull Exact Controllability of Predator - Prey Population Dynamics ∗
The null exact controllability of Predator-prey model with homogeneous Neumann boundary conditions is studied.A carleman type estimate for adjoint linearized system is firstly established.Then we get the controllability of the linearized system. Finally, null exact controlla-bility for the nonlinear problem is obtained using the Kakutani's fixed point theorem.
متن کاملNew conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. III
where λ and m are arbitrary constants and C(U) is an arbitrary smooth function, has been done. The symmetries obtained for constructing exact solutions of the relevant equations have been successfully applied. In the particular case, new exact solutions of nonlinear reactiondiffusion-convection (RDC) equations arising in applications have been found. The most general RDC equation with power fun...
متن کاملConstuction of solitary solutions for nonlinear differential-difference equations via Adomain decomposition method
Here, Adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear differential difference equation and Relativistic Toda couplednonlinear differential-difference equation are chosen to illustrate the validity andthe g...
متن کامل