Regularity of the solutions of the boundary value problems for diffusion-wave equation with generalized functions in right-hand sides

Keywords: fractional derivative, generalized function, boundary value problem, Green vector-function
Published online: 2013-12-30

Abstract


We prove the unique solvability of the first boundary value problem of equation
$$u^{(\beta)}_t-a(t)\Delta u=F(x,t), \;\;\; (x,t) \in (0,l)\times
(0,T],$$

with Riemann-Liouville fractional derivative $u^{(\beta)}_t$ of the order $\beta\in (0,2)$, positive smooth coefficient $a(t)$ and generalized functions in right-hand sides. We obtain some sufficient conditions of the regularity of its solution as variable $t$.

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How to Cite
(1)
LopushanskyA. Regularity of the Solutions of the Boundary Value Problems for Diffusion-Wave Equation With Generalized Functions in Right-Hand Sides. Carpathian Math. Publ. 2013, 5 (2), 279-289.