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Nonlocal convection-diffusion volume-constrained problems and jump processes
1. | Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States |
2. | Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM 87185-1320, United States |
References:
[1] |
F. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. J. Toledo-Melero, Nonlocal Diffusion Problems, Mathematical Surveys and Monographs, 165. American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, 2010. |
[2] |
K. Bogdan, K. Burdzy and Z.-Q. Chen, Censored stable processes, Probability Theory and Related Fields, 127 (2003), 89-152.
doi: 10.1007/s00440-003-0275-1. |
[3] |
N. Burch and R. Lehoucq, Classical, nonlocal, and fractional diffusion equations on bounded domains, International Journal for Multiscale Computational Engineering, 9 (2011), 661-674.
doi: 10.1615/IntJMultCompEng.2011002402. |
[4] |
________, Continuous-time random walks on bounded domains, Physical Review E, 83 (2011), p. 012105. |
[5] |
N. Burch and R. B. Lehoucq, Computing the Exit-Time for a Symmetric Finite-Range Jump Process, Technical report SAND 2013-2354J, Sandia National Laboratories, 2013. |
[6] |
Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, Analysis and approximation of nonlocal diffusion problems with volume constraints, SIAM review, 54 (2012), 667-696.
doi: 10.1137/110833294. |
[7] |
Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, Mathematical Models and Methods in Applied Sciences, 23 (2013), 493-540.
doi: 10.1142/S0218202512500546. |
[8] |
Q. Du, J. Kamm, R. Lehoucq and M. Parks, A new approach for a nonlocal, nonlinear conservation law, SIAM Journal on Applied Mathematics, 72 (2012), 464-487.
doi: 10.1137/110833233. |
[9] |
L. Ignat and J. Rossi, A nonlocal convection-diffusion equation, Journal of Functional Analysis, 251 (2007), 399-437.
doi: 10.1016/j.jfa.2007.07.013. |
[10] |
T. Mengesha and Q. Du, Analysis of a scalar nonlocal peridynamic model with a sign changing kernel, Disc. Cont. Dyn. Sys, B, 18 (2013), 1415-1437.
doi: 10.3934/dcdsb.2013.18.1415. |
show all references
References:
[1] |
F. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. J. Toledo-Melero, Nonlocal Diffusion Problems, Mathematical Surveys and Monographs, 165. American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, 2010. |
[2] |
K. Bogdan, K. Burdzy and Z.-Q. Chen, Censored stable processes, Probability Theory and Related Fields, 127 (2003), 89-152.
doi: 10.1007/s00440-003-0275-1. |
[3] |
N. Burch and R. Lehoucq, Classical, nonlocal, and fractional diffusion equations on bounded domains, International Journal for Multiscale Computational Engineering, 9 (2011), 661-674.
doi: 10.1615/IntJMultCompEng.2011002402. |
[4] |
________, Continuous-time random walks on bounded domains, Physical Review E, 83 (2011), p. 012105. |
[5] |
N. Burch and R. B. Lehoucq, Computing the Exit-Time for a Symmetric Finite-Range Jump Process, Technical report SAND 2013-2354J, Sandia National Laboratories, 2013. |
[6] |
Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, Analysis and approximation of nonlocal diffusion problems with volume constraints, SIAM review, 54 (2012), 667-696.
doi: 10.1137/110833294. |
[7] |
Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, Mathematical Models and Methods in Applied Sciences, 23 (2013), 493-540.
doi: 10.1142/S0218202512500546. |
[8] |
Q. Du, J. Kamm, R. Lehoucq and M. Parks, A new approach for a nonlocal, nonlinear conservation law, SIAM Journal on Applied Mathematics, 72 (2012), 464-487.
doi: 10.1137/110833233. |
[9] |
L. Ignat and J. Rossi, A nonlocal convection-diffusion equation, Journal of Functional Analysis, 251 (2007), 399-437.
doi: 10.1016/j.jfa.2007.07.013. |
[10] |
T. Mengesha and Q. Du, Analysis of a scalar nonlocal peridynamic model with a sign changing kernel, Disc. Cont. Dyn. Sys, B, 18 (2013), 1415-1437.
doi: 10.3934/dcdsb.2013.18.1415. |
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