6 citations · 10 across the 4 of their papers we have counts for
6 papers
Inverse Problems for the Heat Equation with Memory
S. A. Avdonin, S. A. Ivanov, J. M. Wang
We study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Unde…
Singularity Propagation for the Gurtin-Pipkin equation
Sergei Ivanov
We show that the Dirac delta function in the boundary condition of the Gurtin-Pipkin equation generates a moving delta-function with an exponentially decreasing factor.
Regularity of the Gurtin-Pipkin equation
Sergei A. Ivanov
We study regularity of the solution to the Gurtin-Pipkin integral-differential equation of the first order in time. The solution smoothness in Sobolev spaces is proved. Also it…
Spectra of the Gurtin-Pipkin type equations
A. Eremenko, S. Ivanov
We study the spectra of certain integro-differential equations arising in applications. Under some conditions on the kernel of the integral operator, we describe the non-real part…
'Wave type' spectrum of the Gurtin-Pipkin equation of the second order
S. A. Ivanov
We study the complex part of the spectrum of the the Gurtin-Pipkin integral-differential equation of the second order in time. We consider the model case when the kernel is a sum o…
Spectrum of the heat equation with memory
S. Ivanov, T. Sheronova
We consider the Gurtin-Pipkin equation of the first order in time. For the kernel as a series of exponentials we obtain the structure of the spectrum of the system.