LEADER 03557nam 22005775 450 001 9910483188003321 005 20251113201607.0 010 $a3-030-65372-2 024 7 $a10.1007/978-3-030-65372-9 035 $a(CKB)4100000011867181 035 $a(MiAaPQ)EBC6533422 035 $a(Au-PeEL)EBL6533422 035 $a(OCoLC)1246578700 035 $a(PPN)255289618 035 $a(DE-He213)978-3-030-65372-9 035 $a(EXLCZ)994100000011867181 100 $a20210401d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains /$fby Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (xi, 399 pages) 225 1 $aAdvances in Partial Differential Equations,$x2504-3595 ;$v284 311 08$a3-030-65371-4 320 $aIncludes bibliographical references and index. 327 $aElliptic boundary value problems in domains with piecewise smooth boundary -- Wave equation in domains with conical points -- Hyperbolic systems in domains with edges -- Non-stationary Maxwell system in domains with conical points -- Elastodynamics problems in domains with edges -- Wave equation in singularly perturbed domains -- Non-stationary Maxwell system in domains with small holes -- Jermain?Lagrange dynamic plate equation in a domain with corner points. 330 $aThis book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods. 410 0$aAdvances in Partial Differential Equations,$x2504-3595 ;$v284 606 $aMathematical analysis 606 $aApproximation theory 606 $aAnalysis 606 $aApproximations and Expansions 615 0$aMathematical analysis. 615 0$aApproximation theory. 615 14$aAnalysis. 615 24$aApproximations and Expansions. 676 $a515.353 700 $aKorikov$b Dmitrii$01174083 702 $aPlamenevskii?$b B. A. 702 $aSarafanov$b Oleg 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483188003321 996 $aAsymptotic theory of dynamic boundary value problems in irregular domains$92730091 997 $aUNINA