On Determination of Two Time-Dependent Coefficients in a Parabolic Equation
- 54 Downloads
We consider the inverse problem for a one-dimensional parabolic equation with unknown time-depending coefficients of the derivatives with respect to the space variable. We establish a condition for existence of a solution on some time interval whose length depends on the initial data of the problem. Uniqueness of a solution holds on the whole time interval.
KeywordsInitial Data Inverse Problem Parabolic Equation Space Variable
Unable to display preview. Download preview PDF.
- 1.Akhundov A. Ya., “An inverse problem for linear parabolic equations,” Dokl. Akad. Nauk AzSSR, 39, No. 5, 3-6 (1983).Google Scholar
- 2.Muzylev N. V., “Uniqueness theorems for some inverse problems of heat conduction,” Zh. Vychisl. Mat. i Mat. Fiz., 20, No. 2, 388-400 (1980).Google Scholar
- 3.Muzylev N. V., “On unique simultaneous determination of thermal conductivity and specific heat capacity,” Zh. Vychisl. Mat. i Mat. Fiz., 23, No. 1, 102-108 (1983).Google Scholar
- 4.Muzylev N. V., “On uniqueness of solving one inverse problem of linear heat conduction,” Zh. Vychisl. Mat. i Mat. Fiz., 25, No. 9, 1346-1352 (1985).Google Scholar
- 5.Ratyni A. K., “Well-posedness of the problem of determining the matrix of coefficients under leading derivatives in a parabolic equation,” Differentsial'nye Uravneniya, 28, No. 8, 1419-1426 (1992).Google Scholar
- 6.Ivanchov N. I., “On the inverse problem of simultaneous determination of thermal conductivity and specific heat capacity,” Sibirsk. Mat. Zh., 35, No. 3, 612-621 (1994).Google Scholar
- 7.Koval'chuk S. M., “Determination of the coefficient of thermal conductivity and heat capacity per unit in a multilayer medium,” Mat. Metody Fiz.-Mekh. Polya, 40, No. 2, 153-159 (1997).Google Scholar
- 8.Ladyzhenskaya O. A., Solonnikov V. A., and Ural'tseva N. N., Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).Google Scholar
- 9.Ivanchov N. I., “On determination of a time-dependent leading coefficient in a parabolic equation,” Sibirsk. Mat. Zh., 39, No. 3, 539-550 (1998).Google Scholar