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On parabolic Volterra equations in several space dimensions. (English) Zbl 0745.45003
The author obtains Schauder and L p (Q T ) estimates for the solutions to a class of linear parabolic integrodifferential equations. Using these estimates he then studies the continuous dependence, the uniqueness and the regularity of the solutions for a class of nonlinear integrodifferential equations and proves a global solvability result.
Reviewer: I.Vrabie (Iaşi)
MSC:
45K05Integro-partial differential equations
45G10Nonsingular nonlinear integral equations