Determination of source terms in diffusion and wave equations by observations after incidents: uniqueness and stability

We consider a diffusion and a wave equations: $$ \partial_t^ku(x,t) = \Delta u(x,t) + \mu(t)f(x), \quad x\in \Omega, \, t>0, \quad k=1,2 $$ with the zero initial and boundary conditions, where $\Omega \subset \mathbb{R}^d$ is a bounded domain. We establish uniqueness and/or stability results for inverse problems of 1. determining $\mu(t)$, $0

Keywords:

• Stone–Weierstrass theorem
• Mathematical physics
• zero
• Physics
• Eigenfunction
• Uniqueness
• Almost periodic function
• Bounded function
• Fixed point
• Polynomial (hyperelastic model)

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