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Existence and uniqueness of solutions of free boundary problems in heterogeneous environments
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
In this short paper we study the existence and uniqueness of solutions of free boundary problems coming from ecology in heterogeneous environments.
References:
[1] |
J. F. Cao, W. T. Li and M. Zhao,
A nonlocal diffusion model with free boundaries in spatial heterogeneous environment, J. Math. Anal. Appl., 449 (2017), 1015-1035.
doi: 10.1016/j.jmaa.2016.12.044. |
[2] |
Q. L. Chen, F. Q. Li and F. Wang,
The diffusive competition problem with a free boundary in heterogeneous time-periodic environment, J. Math. Anal. Appl., 433 (2016), 1594-1613.
doi: 10.1016/j.jmaa.2015.08.062. |
[3] |
Q. L. Chen, F. Q. Li and F. Wang,
A reaction-diffusion-advection competition model with two free boundaries in heterogeneous time-periodic environment, IMA J. Appl. Math., 82 (2017), 445-470.
doi: 10.1093/imamat/hxw059. |
[4] |
Y. H. Du and Z. G. Lin,
Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[5] |
C. X. Lei and Y. H. Du,
Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model, Discrete Contin. Dyn. Syst. B, 22 (2017), 895-911.
doi: 10.3934/dcdsb.2017045. |
[6] |
H. Monobe and C-H. Wu,
On a free boundary problem for a reaction-diffusion-advection logistic model in heterogeneous environment, J. Differential Equations, 261 (2016), 6144-6177.
doi: 10.1016/j.jde.2016.08.033. |
[7] |
J. Wang and L. Zhang,
Invasion by an inferior or superior competitor: A diffusive competition model with a free boundary in a heterogeneous environment, J. Math. Anal. Appl., 423 (2015), 377-398.
doi: 10.1016/j.jmaa.2014.09.055. |
[8] |
M. X. Wang, Sobolev Spaces, (in Chinese), Higher Education Press, Bejing, 2013. |
[9] |
M. X. Wang,
The diffusive logistic equation with a free boundary and sign-changing coefficient, J. Differential Equations, 258 (2015), 1252-1266.
doi: 10.1016/j.jde.2014.10.022. |
[10] |
M. X. Wang,
A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment, J. Funct. Anal., 270 (2016), 483-508.
doi: 10.1016/j.jfa.2015.10.014. |
[11] |
M. X. Wang, Nonlinear Second Order Parabolic Equations, in: Lecture Notes. |
[12] |
M. X. Wang and Y. Zhang, The time-periodic diffusive competition models with a free boundary and sign-changing growth rates, Z. Angew. Math. Phys., 67 (2016), Art. 132, 24 pp.
doi: 10.1007/s00033-016-0729-9. |
[13] |
M. X. Wang and J. F. Zhao,
A free boundary problem for a predator-prey model with double free boundaries, J. Dyn. Diff. Equat., 29 (2017), 957-979.
doi: 10.1007/s10884-015-9503-5. |
[14] |
J. F. Zhao and M. X. Wang,
A free boundary problem of a predator-prey model with higher dimension and heterogeneous environment, Nonlinear Anal.: Real World Appl., 16 (2014), 250-263.
doi: 10.1016/j.nonrwa.2013.10.003. |
[15] |
M. Zhao, W. T. Li and J. F. Cao,
A prey-predator model with a free boundary and sign-changing coefficient in time-periodic environment, Discrete Cont. Dyn. Syst. B, 22 (2017), 3295-3316.
doi: 10.3934/dcdsb.2017138. |
[16] |
Y. G. Zhao and M. X. Wang,
Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients, IMA J. Appl. Math., 81 (2016), 255-280.
doi: 10.1093/imamat/hxv035. |
[17] |
L. Zhou, S. Zhang and Z. H. Liu,
An evolutional free-boundary problem of a reaction-diffusion-advection system, Proc. Royal Soc. Edinburgh A, 147 (2017), 615-648.
doi: 10.1017/S0308210516000226. |
show all references
References:
[1] |
J. F. Cao, W. T. Li and M. Zhao,
A nonlocal diffusion model with free boundaries in spatial heterogeneous environment, J. Math. Anal. Appl., 449 (2017), 1015-1035.
doi: 10.1016/j.jmaa.2016.12.044. |
[2] |
Q. L. Chen, F. Q. Li and F. Wang,
The diffusive competition problem with a free boundary in heterogeneous time-periodic environment, J. Math. Anal. Appl., 433 (2016), 1594-1613.
doi: 10.1016/j.jmaa.2015.08.062. |
[3] |
Q. L. Chen, F. Q. Li and F. Wang,
A reaction-diffusion-advection competition model with two free boundaries in heterogeneous time-periodic environment, IMA J. Appl. Math., 82 (2017), 445-470.
doi: 10.1093/imamat/hxw059. |
[4] |
Y. H. Du and Z. G. Lin,
Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[5] |
C. X. Lei and Y. H. Du,
Asymptotic profile of the solution to a free boundary problem arising in a shifting climate model, Discrete Contin. Dyn. Syst. B, 22 (2017), 895-911.
doi: 10.3934/dcdsb.2017045. |
[6] |
H. Monobe and C-H. Wu,
On a free boundary problem for a reaction-diffusion-advection logistic model in heterogeneous environment, J. Differential Equations, 261 (2016), 6144-6177.
doi: 10.1016/j.jde.2016.08.033. |
[7] |
J. Wang and L. Zhang,
Invasion by an inferior or superior competitor: A diffusive competition model with a free boundary in a heterogeneous environment, J. Math. Anal. Appl., 423 (2015), 377-398.
doi: 10.1016/j.jmaa.2014.09.055. |
[8] |
M. X. Wang, Sobolev Spaces, (in Chinese), Higher Education Press, Bejing, 2013. |
[9] |
M. X. Wang,
The diffusive logistic equation with a free boundary and sign-changing coefficient, J. Differential Equations, 258 (2015), 1252-1266.
doi: 10.1016/j.jde.2014.10.022. |
[10] |
M. X. Wang,
A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment, J. Funct. Anal., 270 (2016), 483-508.
doi: 10.1016/j.jfa.2015.10.014. |
[11] |
M. X. Wang, Nonlinear Second Order Parabolic Equations, in: Lecture Notes. |
[12] |
M. X. Wang and Y. Zhang, The time-periodic diffusive competition models with a free boundary and sign-changing growth rates, Z. Angew. Math. Phys., 67 (2016), Art. 132, 24 pp.
doi: 10.1007/s00033-016-0729-9. |
[13] |
M. X. Wang and J. F. Zhao,
A free boundary problem for a predator-prey model with double free boundaries, J. Dyn. Diff. Equat., 29 (2017), 957-979.
doi: 10.1007/s10884-015-9503-5. |
[14] |
J. F. Zhao and M. X. Wang,
A free boundary problem of a predator-prey model with higher dimension and heterogeneous environment, Nonlinear Anal.: Real World Appl., 16 (2014), 250-263.
doi: 10.1016/j.nonrwa.2013.10.003. |
[15] |
M. Zhao, W. T. Li and J. F. Cao,
A prey-predator model with a free boundary and sign-changing coefficient in time-periodic environment, Discrete Cont. Dyn. Syst. B, 22 (2017), 3295-3316.
doi: 10.3934/dcdsb.2017138. |
[16] |
Y. G. Zhao and M. X. Wang,
Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients, IMA J. Appl. Math., 81 (2016), 255-280.
doi: 10.1093/imamat/hxv035. |
[17] |
L. Zhou, S. Zhang and Z. H. Liu,
An evolutional free-boundary problem of a reaction-diffusion-advection system, Proc. Royal Soc. Edinburgh A, 147 (2017), 615-648.
doi: 10.1017/S0308210516000226. |
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