Parabolic-Type Integrodifferential Equations

Abstract

The study of many physical processes arising in science and engineering leads to the models of parabolic integrodifferential equations with different initial boundary conditions. These equations occur in several applications, such as in heat flow in materials with memory, control and optimization theories, reaction diffusion processes, epidemic models and various other fields of science and technology. Considerable research on the special kinds of parabolic integrodifferential equations has been carried out by using new mathematical ideas, approaches, and theories, see [1,5,8,9,31–33,59–62,74,80,98,110,121,122,124,126,127,132,140,141] and the references given therein. The main goal of this chapter is to discuss the wellposedness related to certain nonlinear parabolic integrodifferential equations studied in [109,110,75,77,140]. There are other topics related to such equations, which we did not include here due to space limitation e.g., see the references quoted in [1,5,25,26,39,45,60,61,80,121,122,124,126,137,141]. A detailed survey, including comprehensive list of references of the early developments to the topic can be found in the monograph [5].