TY - CHAP
T1 - Non-Linear Evolution Equations with Non-Local Coefficients and Zero-Neumann Condition
T2 - One Dimensional Case
AU - Kubo, Akisato
AU - Hoshino, Hiroki
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.
PY - 2023
Y1 - 2023
N2 - In this paper, we investigate the global existence in time and asymptotic behaviour of solutions of non-linear evolution equations with strong dissipation and non-local coefficients in one spacial dimension, arising in mathematical models of cell migration. We consider the initial boundary value problem with zero-Neumann condition for the equation, applying the argument of the singular integral operator to the non-local term, and we obtain the L2 -estimate of it which is necessary for the energy estimates of our problems. Finally we can prove the desired result by the standard argument of the interation scheme of our problem.
AB - In this paper, we investigate the global existence in time and asymptotic behaviour of solutions of non-linear evolution equations with strong dissipation and non-local coefficients in one spacial dimension, arising in mathematical models of cell migration. We consider the initial boundary value problem with zero-Neumann condition for the equation, applying the argument of the singular integral operator to the non-local term, and we obtain the L2 -estimate of it which is necessary for the energy estimates of our problems. Finally we can prove the desired result by the standard argument of the interation scheme of our problem.
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U2 - 10.1007/978-3-031-36375-7_49
DO - 10.1007/978-3-031-36375-7_49
M3 - Chapter
AN - SCOPUS:85176563811
T3 - Trends in Mathematics
SP - 647
EP - 658
BT - Trends in Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -