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

Authors

  • A.O. Lopushansky Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-1448-964X
https://doi.org/10.15330/cmp.5.2.279-289

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)
Lopushansky, A. 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, 279-289.