TY - JOUR
T1 - Semi-linear Cauchy problem and Markov process associated with a p-adic non-local ultradiffusion operator
AU - Casas-Sánchez, O. F.
AU - Chacón-Cortés, L. F.
AU - Galeano-Peñaloza, J.
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - This work is dedicated to study the pseudodifferential operator (Dd1,d2αφ)(x)=-∫QpnAd1,d2-α(y)[φ(x+y)-φ(x)]dny, which can be seen as a generalization of Taibleson operator; here Ad1,d2α(x)=max{∥x∥pd1,∥x∥pd2}α. We show that semi-linear Cauchy problem is well-posed in Mλ [a Banach space containing functions that do not belong to L1(Qpn)], assuming that semi-linear part f is a Lipschitz function. We associate to the corresponding homogeneous problem a Markov process, which is indeed a Feller process. Finally, we study the first passage time problem.
AB - This work is dedicated to study the pseudodifferential operator (Dd1,d2αφ)(x)=-∫QpnAd1,d2-α(y)[φ(x+y)-φ(x)]dny, which can be seen as a generalization of Taibleson operator; here Ad1,d2α(x)=max{∥x∥pd1,∥x∥pd2}α. We show that semi-linear Cauchy problem is well-posed in Mλ [a Banach space containing functions that do not belong to L1(Qpn)], assuming that semi-linear part f is a Lipschitz function. We associate to the corresponding homogeneous problem a Markov process, which is indeed a Feller process. Finally, we study the first passage time problem.
KW - First passage time
KW - Taibleson operator
KW - Ultradiffusion
KW - p-adic numbers
UR - http://www.scopus.com/inward/record.url?scp=85081886795&partnerID=8YFLogxK
U2 - 10.1007/s11868-020-00334-2
DO - 10.1007/s11868-020-00334-2
M3 - Article
AN - SCOPUS:85081886795
SN - 1662-9981
VL - 11
SP - 1085
EP - 1110
JO - Journal of Pseudo-Differential Operators and Applications
JF - Journal of Pseudo-Differential Operators and Applications
IS - 3
ER -