TY - JOUR
T1 - The Solvability for a Class of Nonlinear Integrodifferential Equations of Parabolic Type
AU - Yin Hongming
JO - Journal of Partial Differential Equations
VL - 3
SP - 46
EP - 60
PY - 1992
DA - 1992/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5744.html
KW - Integrodifferential equation
KW -  nonlinearity
KW -  global solvability
AB -  In this paper we consider the well-posedness for a class of nonlinear integrodifferential equations of parabolic type. We use integral estimates to deduce an a priori estimate in the classical space C^{2+&#945,1+\frac{&#945}{2}}. The existence of the solution is established by means of the continuity method which is similar to a parabolic initial and boundary value problem. Moreover, the continuous dependence upon the data and the uniqueness of the solution are obtained. Finally, the results are generalized into a class of nonlinear integrodifferential systems.