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On a time-discretization method for a semilinear heat equation with purely integral conditions in a nonclassical function space. (English) Zbl 1105.35044

Summary: We construct a semidiscrete approximate solution to a semilinear one-dimensional heat equation subject to integral boundary conditions by means of the Rothe discretization in time method. The convergence of the approximation scheme obtained is proved, yielding the well-posedness of the problem considered.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B45 A priori estimates in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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