Inverse boundary value problems for diffusion-wave equation with generalized functions in right-hand sides

  • A.O. Lopushansky Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-1448-964X
  • H.P. Lopushanska Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
Keywords: fractional derivative, inverse boundary value problem, Green vector-function, operator equation
Published online: 2014-07-14

Abstract


We prove the unique solvability of the problem on determination of the solution $u(x,t)$ of the first boundary value problem for equation

$$u^{(\beta)}_t-a(t)\Delta u=F_0(x)\cdot g(t), \;\;\; (x,t) \in (0,l)\times
(0,T],$$

with fractional derivative $u^{(\beta)}_t$ of the order $\beta\in (0,2)$, generalized functions in initial conditions, and also determination of unknown continuous coefficient $a(t)>0, \; t\in [0,T]$ (or unknown continuous function $g(t)$) under given the values $(a(t)u_x(\cdot,t),\varphi_0(\cdot))$ ($(u(\cdot,t),\varphi_0(\cdot))$, respectively) of according generalized function onto some test function $\varphi_0(x)$.

Article metrics
PDF downloads: 18
Abstract views: 67