TY - JOUR
T1 - Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations
JO - Journal of Partial Differential Equations
VL - 4
SP - 301
EP - 312
PY - 1998
DA - 1998/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5572.html
KW - Multipliers
KW - parabolic type equations
KW - Cauchy problem
KW - initial boundary value problem
KW - space-time estimate
AB -  In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space.