Controllability Of Semilinear Heat Equation Research Articles

Approximate Controllability of Semilinear Heat Equation with Noninstantaneous Impulses, Memory, and Delay

Approximate Controllability of Semilinear Heat Equation with Noninstantaneous Impulses, Memory, and Delay

Rothe’s Fixed Point Theorem and the Approximate Controllability of Semilinear Heat Equation with Impulses, Delays, and Nonlocal Conditions

Rothe’s Fixed Point Theorem and the Approximate Controllability of Semilinear Heat Equation with Impulses, Delays, and Nonlocal Conditions

Null controllability for semilinear heat equation with dynamic boundary conditions

<p style='text-indent:20px;'>This paper deals with the null controllability of the semilinear heat equation with dynamic boundary conditions of surface diffusion type, with nonlinearities involving drift terms. First, we prove a negative result for some function <inline-formula><tex-math id="M1">\begin{document}$ F $\end{document}</tex-math></inline-formula> that behaves at infinity like <inline-formula><tex-math id="M2">\begin{document}$ |s| \ln ^{p}(1+|s|), $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M3">\begin{document}$ p > 2 $\end{document}</tex-math></inline-formula>. Then, by a careful analysis of the linearized system and a fixed point method, a null controllability result is proved for nonlinearties <inline-formula><tex-math id="M4">\begin{document}$ F(s, \xi) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ G(s, \xi) $\end{document}</tex-math></inline-formula> growing slower than <inline-formula><tex-math id="M6">\begin{document}$ |s| \ln ^{3 / 2}(1+|s|+\|\xi\|)+\|\xi\| \ln^{1 / 2}(1+|s|+\|\xi\|) $\end{document}</tex-math></inline-formula> at infinity.</p>

Controllability for semilinear heat equation with globally Lipschitz nonlinearities and memory term

In this paper, we investigate the controllability for a semilinear heat equation with memory and internal control in a bounded domain of Rn. The semilinearity has gradient terms and is globally Lipschitzian. Since memory term does not allow applying Fabre’s unique continuation theorem directly, we made certain adjustments to the terms of the equation. Additionally, the proof of the controllability uses a variant of a classic fixed point method and a technique due to Zuazua and Fabre-Puel-Zuazua.

Finite approximate controllability for semilinear heat equations in noncylindrical domains

We investigate finite approximate controllability for semilinear heat equation in noncylindrical domains. First we study the linearized problem and then by an application of the fixed point result of Leray-Schauder we obtain the finite approximate controllability for the semilinear state equation.

Global Approximately Controllability and Finite Dimensional Exact Controllability of Semilinear Heat Equation in R N

We prove the approxomate controllability and finite dimensional exact controllability of semilinear heat equation in R N with the same control by introducing the weighted Soblev spaces.

Remarks on null controllability for semilinear heat equation in moving domains

We investigate in this article the null controllability for the semilinear heat operator u 0 u + f(u) in a domain which boundary is moving with the time t.