Geodesic
Inverse Problems of Finding the Absorption Parameter in the Diffusion Equation
Matematičeskie zametki, Tome 106 (2019) no. 3, pp. 395-408

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The paper is devoted to the study of inverse problems of finding, together with a solution $u(x,t)$ of the diffusion equation $$ u_t-\Delta u +[c(x,t)+aq_0(x,t)]u=f(x,t), $$ the parameter $a$ characterizing absorption ($c(x,t)$ and $q_0(x,t)$ are given functions). It is assumed that, on the function $u(x,t)$, nonpercolation conditions and some special overdetermination conditions of integral form are imposed. We prove existence theorems for solutions $(u(x,t),a)$ such that the function $u(x,t)$ has all Sobolev generalized derivatives appearing in the equation and $a$ is a nonnegative number.
Mots-clés : diffusion equation, existence.
Keywords: nonpercolation condition, unknown parameter, inverse problems, final integral overdetermination conditions 
@article{MZM_2019_106_3_a6,
     author = {A. I. Kozhanov},
     title = {Inverse {Problems} of {Finding} the {Absorption} {Parameter} in the {Diffusion} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {395--408},
     publisher = {mathdoc},
     volume = {106},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_3_a6/}
}
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A. I. Kozhanov. Inverse Problems of Finding the Absorption Parameter in the Diffusion Equation. Matematičeskie zametki, Tome 106 (2019) no. 3, pp. 395-408. http://geodesic.mathdoc.fr/item/MZM_2019_106_3_a6/