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The Westervelt equation with a causal propagation operator coupled to the bioheat equation.
Recasting a Brinkman-based acoustic model as the damped Burgers equation
1. | University of New Orleans, Department of Physics, New Orleans, LA 70148, United States, United States |
References:
[1] |
J. D. Cole, On a quasi-linear parabolic equation occuring in aerodynamics, Quarterly of Applied Mathematics, 9 (1951), 225-236. |
[2] |
D. G. Crighton, Model equations of nonlinear acoustics, Annual Review of Fluid Mechanics, 11 (1979), 11-33.
doi: 10.1146/annurev.fl.11.010179.000303. |
[3] |
P. M. Jordan, A survey of weakly-nonlinear acoustic models: 1910-2009, Mechanics Research Communications, 73 (2016), 127-139.
doi: 10.1016/j.mechrescom.2016.02.014. |
[4] |
P. M. Jordan, Some remarks on nonlinear poroacoustic phenomena, Mathematics and Computers in Simulation (MATCOM), 80 (2009), 202-211.
doi: 10.1016/j.matcom.2009.06.004. |
[5] |
S. V. Korsunskii, Propagation of nonlinear magnetoacoustic waves in electrically conductlnq dissipative media with drag, Sov. Phys. Acoust., 37 (1991), 373-375. |
[6] |
W. Malfiet, Approximate solution of the damped Burgers equation, Journal of Physics A: Mathematical and General, 26 (1993), L723-L728. |
[7] |
D. A. Nield and A. Bejan, Convection in Porous Media, $2^{nd}$ edition, Springer, New York, 1999.
doi: 10.1007/978-1-4757-3033-3. |
[8] |
L. E. Payne, J. Rodrigues and B. Straughan, Effect of anisotropic permeability on Darcy's law, Mathematical Methods in the Applied Sciences, 24 (2001), 427-438.
doi: 10.1002/mma.228. |
[9] |
D. A. Rossmanith and A. Puri, The role of Brinkman viscosity in poroacoustic propagation, International Journal of Non-Linear Mechanics, 67 (2014), 1-6.
doi: 10.1016/j.ijnonlinmec.2014.07.002. |
[10] |
D. A. Rossmanith and A. Puri, Non-linear evolution of a sinusoidal pulse under a Brinkman-based poroacoustic model, International Journal of Non-Linear Mechanics, 78 (2016), 53-58.
doi: 10.1016/j.ijnonlinmec.2015.09.014. |
[11] |
S. I. Soluyan and R. V. Khokhlov, Finite amplitude acoustic waves in a relaxing medium, Sov. Phys. Acoust., 8 (1962), 170-175. |
[12] |
P. A. Thompson, Compressible-fluid Dynamics, McGraw-Hill, New York, 1972. |
show all references
References:
[1] |
J. D. Cole, On a quasi-linear parabolic equation occuring in aerodynamics, Quarterly of Applied Mathematics, 9 (1951), 225-236. |
[2] |
D. G. Crighton, Model equations of nonlinear acoustics, Annual Review of Fluid Mechanics, 11 (1979), 11-33.
doi: 10.1146/annurev.fl.11.010179.000303. |
[3] |
P. M. Jordan, A survey of weakly-nonlinear acoustic models: 1910-2009, Mechanics Research Communications, 73 (2016), 127-139.
doi: 10.1016/j.mechrescom.2016.02.014. |
[4] |
P. M. Jordan, Some remarks on nonlinear poroacoustic phenomena, Mathematics and Computers in Simulation (MATCOM), 80 (2009), 202-211.
doi: 10.1016/j.matcom.2009.06.004. |
[5] |
S. V. Korsunskii, Propagation of nonlinear magnetoacoustic waves in electrically conductlnq dissipative media with drag, Sov. Phys. Acoust., 37 (1991), 373-375. |
[6] |
W. Malfiet, Approximate solution of the damped Burgers equation, Journal of Physics A: Mathematical and General, 26 (1993), L723-L728. |
[7] |
D. A. Nield and A. Bejan, Convection in Porous Media, $2^{nd}$ edition, Springer, New York, 1999.
doi: 10.1007/978-1-4757-3033-3. |
[8] |
L. E. Payne, J. Rodrigues and B. Straughan, Effect of anisotropic permeability on Darcy's law, Mathematical Methods in the Applied Sciences, 24 (2001), 427-438.
doi: 10.1002/mma.228. |
[9] |
D. A. Rossmanith and A. Puri, The role of Brinkman viscosity in poroacoustic propagation, International Journal of Non-Linear Mechanics, 67 (2014), 1-6.
doi: 10.1016/j.ijnonlinmec.2014.07.002. |
[10] |
D. A. Rossmanith and A. Puri, Non-linear evolution of a sinusoidal pulse under a Brinkman-based poroacoustic model, International Journal of Non-Linear Mechanics, 78 (2016), 53-58.
doi: 10.1016/j.ijnonlinmec.2015.09.014. |
[11] |
S. I. Soluyan and R. V. Khokhlov, Finite amplitude acoustic waves in a relaxing medium, Sov. Phys. Acoust., 8 (1962), 170-175. |
[12] |
P. A. Thompson, Compressible-fluid Dynamics, McGraw-Hill, New York, 1972. |
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