TY - JOUR
T1 - Largest well-posed spaces for the general diffusion system with nonlocal interactions
AU - Deng, Chao
AU - Liu, Chun
N1 - Funding Information:
Chao Deng is supported by the NSF of Jiangsu Province (No. BK20130225), the NSFC (No. 11301228); he is also partially supported by NSFC (Nos. 11171357, 11271166, 11271167). This joint work was done during Chao Deng's visit to the Pennsylvania State University (PSU). He would like to express his gratitude to the Math Department of PSU for their kindness. Chun Liu wishes to acknowledge the partial support by the National Science Foundation grants DMS-1109107, DMS-1216938, and DMS-1159937.
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/5/15
Y1 - 2017/5/15
N2 - The authors derive a general diffusion (GD) system with nonlocal interactions of special structure via energetic variational approach and observe that there exist two critical values of s, i.e. s=12,1, for the nonlocal interactions, where s=12 reflects how strong nonlocal property we have and s=1 affects the linearization and choice of initial data spaces. The authors also establish the global existence and uniqueness of mild solution.
AB - The authors derive a general diffusion (GD) system with nonlocal interactions of special structure via energetic variational approach and observe that there exist two critical values of s, i.e. s=12,1, for the nonlocal interactions, where s=12 reflects how strong nonlocal property we have and s=1 affects the linearization and choice of initial data spaces. The authors also establish the global existence and uniqueness of mild solution.
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U2 - 10.1016/j.jfa.2017.02.001
DO - 10.1016/j.jfa.2017.02.001
M3 - Article
AN - SCOPUS:85012908937
SN - 0022-1236
VL - 272
SP - 4030
EP - 4062
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 10
ER -