The classical solutions for nonlinear parabolic integrodifferential equations
The paper deals with the solvability and regularity (in the classical sense) of the initial-boundary value problem for the nonlinear partial integrodifferential equation \[ u_ t=a(x,t,u,u_ x)u_{xx}+b(x,t,u,u_ x)+\int^{t}_{0}c(x,s,u,u_ x)ds, \] \(x\in (0,1)\times (0,T)\); \(u(i,t)=f_ i(t)\), \(t\in [0,T]\), \(i=0,1\); \(u(x,0)=u^ 0(x)\), \(x\in [0,1]\). Uniqueness and continuous dependence of the solution (on the data \(f_ i\), \(u^ 0)\) is also established.
scientific article; zbMATH DE number 4098022