M. Salman

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20152020

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math.AP2020

A Diffusion Problem with Neumann Boundary Control Utilizing Total Mass

M. Salman

The author studies the diffusion problem $u_{t} = u_{xx}, 0 < x < 1, t > 0; u (x, 0) = 0,$ and $- u_{x} (0, t) = u_{x} (1, t) = ϕ (t),$ where $ϕ (t)$ is a control function that ensures that the total mass…

math.AP2020

The utilization of total mass to determine the switching points in the symmetric boundary control of a diffusion problem

Mohamed Salman

The authors study the problem $u_{t} = u_{xx}, 0 < x < 1, t > 0; u (x, 0) = 0,$ and $u (0, t) = u (1, t) = ψ (t),$ where $ψ (t) = u_{0}$ for $t_{2 k} < t < t_{2 k + 1}$ and $ψ (t) = 0$ for $t_{2k+1} <t<t_{2k+2},\…