TY - JOUR
T1 - Remarks on global solutions to the cauchy problem for semirelativistic equations with power type nonlinearity
AU - Fujiwara, Kazumasa
AU - Ozawa, Tohru
N1 - Funding Information:
The research of Fujiwara was partly supported by the Japan Society for the Promotion of Science, Grant-in-Aid for JSPS Fellows no 26.7371.
Publisher Copyright:
© 2015 Kazumasa Fujiwara and Tohru Ozawa.
PY - 2015
Y1 - 2015
N2 - Existence and nonexistence results on global solutions to the Cauchy problem for semirelativistic equations are shown by a simple compact- ness argument and a test function method, respectively. To obtain the nonexistence of global solutions, semirelativistic equations are trans- formed into a new equation without nonlocal operators in linear part but with a time derivative in nonlinear part, which is shown to be under control of special choice of test functions.
AB - Existence and nonexistence results on global solutions to the Cauchy problem for semirelativistic equations are shown by a simple compact- ness argument and a test function method, respectively. To obtain the nonexistence of global solutions, semirelativistic equations are trans- formed into a new equation without nonlocal operators in linear part but with a time derivative in nonlinear part, which is shown to be under control of special choice of test functions.
KW - Compactness argument
KW - Nonexistence of weak solutions
KW - Semirelativistic equation
KW - Test function method
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U2 - 10.12988/ijma.2015.58211
DO - 10.12988/ijma.2015.58211
M3 - Article
AN - SCOPUS:84953391437
SN - 1312-8876
VL - 9
SP - 2599
EP - 2610
JO - International Journal of Mathematical Analysis
JF - International Journal of Mathematical Analysis
IS - 53-56
ER -