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

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.

### MSC:

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

### Keywords:

heat conductivity equation; thermal memory; inverse problem
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