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Quasi-linearisation methods for a nonlinear heat equation with functional dependence. (English) Zbl 0964.35075

The author considers a heat equation with the nonlinear right-hand side which depends on Volterra-type functionals acting on the unknown function and on its gradient. Some natural sufficient conditions for the existence and uniqueness of solutions to this equation are given. The solution is obtained as a limit of a fast convergent sequence of successive approximations obtained by the quasilinearization method.

MSC:

35K55 Nonlinear parabolic equations
35A35 Theoretical approximation in context of PDEs
35K10 Second-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35K15 Initial value problems for second-order parabolic equations
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