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- W2401792613 abstract "Let (varOmega subset mathbb{R}^{n}) be a bounded domain with a smooth boundary or (varOmega = mathbb{R}^{n}.) This chapter discusses well-posedness problems of general boundary value problems for pseudo-differential and differential-operator equations of the form $$displaystylebegin{array}{rcl} L[u]& equiv & frac{partial ^{m}u} {partial t^{m}} +sum _{ k=0}^{m-1}A_{ k}(t)frac{partial ^{k}u} {partial t^{k}} = f(t,x),quad t in (T_{1},T_{2}), x in varOmega,{}end{array}$$(4.1)$$displaystylebegin{array}{rcl} B_{k}[u]& equiv & sum _{j=0}^{m-1}b_{ kj}frac{partial ^{j}u(t_{kj},x)} {partial t^{j}} =varphi _{k}(x),quad x in varOmega,,k = 0,mathop{ldots },m - 1,{}end{array}$$(4.2)where f(t, x) is defined on ((T_{1},T_{2})times varOmega,) (-infty <T_{1} <T_{2} leq infty,) and (varphi _{k}(x),,x in varOmega,,k = 0,ldots,m - 1,) are given functions; A k (t) and b kj , (k = 0,ldots,m - 1,,j = 0,ldots,m - 1,) are operators acting on some spaces (specified below) of functions defined on Ω; and (t_{jk} in [T_{1},T_{2}],,j,k = 0,ldots,m - 1.) For example, when (varOmega = mathbb{R}^{n},) the latter operators may act as ΨDOSS defined on the space of distributions (varPsi _{-G,p^{'}}^{'}(mathbb{R}^{n})) with an appropriate (G subset R^{n})." @default.
- W2401792613 created "2016-06-24" @default.
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- W2401792613 date "2015-01-01" @default.
- W2401792613 modified "2023-09-24" @default.
- W2401792613 title "Boundary value problems for pseudo-differential equations with singular symbols" @default.
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- W2401792613 doi "https://doi.org/10.1007/978-3-319-20771-1_4" @default.
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