Cauchy problem for nonlocal diffusion equations modelling Lévy flights
In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First, the asymptotic behavior of the fundamental s...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciáloperátor, Differenciálegyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.18 |
| Online Access: | http://acta.bibl.u-szeged.hu/75833 |
| Tartalmi kivonat: | In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First, the asymptotic behavior of the fundamental solution of the fractional diffusion equation is considered. Then, we use the fundamental solution to obtain the representation formula of solutions of the Cauchy problem. In the last, the L 2 -decay estimates for solutions are proved by employing the Fourier analysis technique. |
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| Terjedelem/Fizikai jellemzők: | 22 |
| ISSN: | 1417-3875 |