Heat equation with degeneration in Holder and Slobodetskii spaces
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We study initial-boundary value problems for the heat equation in which heat conductivity α2(x) may depend on the space variablex ∈ ℝ+; the nonnegative functionα(x) is allowed to tend to infinity (respectively, zero) asx → +∞ (respectively,x → +0). We prove that these problems are well posed and examine the smoothness of solutions. It is shown that criteria for smoothness of the solutions can be stated in terms of certain functionals, namely, the Hölder constant (for Hölder spaces) and the generalized Hölder constant (for Slobodetskii spaces).
KeywordsHeat Conductivity Heat Equation Slobodetskii Space
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