We prove well-posedness for general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various condi- tions in the vertices. More precisely, using the theory of strongly continuous operator semigroups we show that a large class of (not necessarily self-adjoint) second order differential operators with general (possibly non-local) bound- ary conditions generate cosine families, hence also analytic semigroups, on L^p (R + , C ` ) × L^p ([0, 1], C m ) for 1 ≤ p < +∞.
WAVES AND DIFFUSION ON METRIC GRAPHS WITH GENERAL VERTEX CONDITIONS
Klaus-Jochen Engel
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2019-01-01
Abstract
We prove well-posedness for general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various condi- tions in the vertices. More precisely, using the theory of strongly continuous operator semigroups we show that a large class of (not necessarily self-adjoint) second order differential operators with general (possibly non-local) bound- ary conditions generate cosine families, hence also analytic semigroups, on L^p (R + , C ` ) × L^p ([0, 1], C m ) for 1 ≤ p < +∞.File in questo prodotto:
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