Problem of determining a multidimensional thermal memory in a heat conductivity equation. (English) Zbl 1449.35426

Durdiev, D. K.; Zhumaev, Zh. Zh.

Methods Funct. Anal. Topol. 25, No. 3, 218-225 (2019).

The authors study the problem of determining the functions \(u(x,t)\), \(K(x',t)\), \(x=(x_1,x_2,\ldots ,x_{n-1},x_n)=(x',x_n)\in \mathbb{R}^n\), \(t>0\), from the equation \[ u_t-\Delta u=\int\limits_0^t K(x',t-\tau)\Delta u(x, \tau)\,d\tau,\quad x\in \mathbb{R}^n,t\in [0,T], \] with appropriate initial and boundary conditions. The existence and uniqueness results are obtained.

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

35R09	Integro-partial differential equations
35R30	Inverse problems for PDEs

Keywords:

heat conductivity equation; thermal memory; inverse problem