Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  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.  first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then this result is successfully used with some estimates for parabolic equation in L k  spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model.
['Kumarasamy Sakthivel', 'Krishnan Balachandran', 'Jong Yeoul Park', 'G. Devipriya']
I am writing a research paper on a idea NULL CONTROLLABILITY OF A NONLINEAR DIFFUSION SYSTEM IN REACTOR DYNAMICS
[{"from": "human", "value": "I am writing a research paper on a idea NULL CONTROLLABILITY OF A NONLINEAR DIFFUSION SYSTEM IN REACTOR DYNAMICS"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  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 \u211d with a distributed control acting on a subinterval.  first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then this result is successfully used with some estimates for parabolic equation in L k  spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model."}]