Abstract
In this chapter we shall consider second-order parabolic equations and prove the unique solvability of the initial-boundary value problem in the domains Q T =, (x, t): x ∈ Ω,t ∈ (0, T) for the first, second, and third boundary conditions. We shall assume that the domain Ω is bounded, although all the results, except for the representation of solutions by Fourier series, will be valid for an arbitrary unbounded domain Ω. Moreover, the methods of solution given for bounded Ω are applicable to unbounded Ω (in particular, for Ω = R n),but need minor modification which we shall point out.
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© 1985 Springer Science+Business Media New York
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Ladyzhenskaya, O.A. (1985). Equations of Parabolic Type. In: The Boundary Value Problems of Mathematical Physics. Applied Mathematical Sciences, vol 49. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4317-3_3
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DOI: https://doi.org/10.1007/978-1-4757-4317-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2824-5
Online ISBN: 978-1-4757-4317-3
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