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The classical solutions for nonlinear parabolic integrodifferential equations. (English) Zbl 0671.45004
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.
Reviewer: S.Milusheva

MSC:
 45K05 Integro-partial differential equations 45G10 Other nonlinear integral equations
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