{"94d75063978007fd2183af88d8431c63elkepeter":{"DOI":"10.1007/s10231-020-00950-1","ISBN":"","ISSN":"0373-3114","URL":"https://doi.org/10.1007/s10231-020-00950-1","abstract":"The authors consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is bounded from below by an impermeable horizontal bed. Three equivalent classical formulations in a suitable setting of strong solutions which may describe nevertheless waves with singular density gradients are established. The availability of a weak formulation of the water wave problem, the regularity properties of the corresponding weak solutions, and methods from nonlinear functional analysis are used. The paper is organized as follows. In Section 2, the three formulations of the problem are introduced and their equivalence is established. In Section 3, the authors first introduce the notion of a weak solution to Dubreil-Jacotin's formulation and establish, by means of a shooting method, the existence of at least one laminar flow solution to this latter formulation. In Section 4, the equations are reformulated as an abstract bifurcation problem by using methods from nonlinear functional analysis.","annote":"","author":[{"family":"Escher","given":"Joachim"},{"family":"Knopf","given":"Patrik"},{"family":"Lienstromberg","given":"Christina"},{"family":"Matioc","given":"Bogdan-Vasile"}],"citation-label":"MR4142857","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Ann. Mat. Pura Appl. (4)","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2020"]],"literal":"2020"},"event-place":"","id":"94d75063978007fd2183af88d8431c63elkepeter","interhash":"f49cedf1153177fe651e0670050bf616","intrahash":"94d75063978007fd2183af88d8431c63","issue":"5","issued":{"date-parts":[["2020"]],"literal":"2020"},"keyword":"Lienstromberg gradients singular density","misc":{"mrclass":"76B15 (35B32 35C07 35Q35 76B70)","mrreviewer":"Gheorghe Procopiuc","fjournal":"Annali di Matematica Pura ed Applicata. Series IV","mrnumber":"4142857","issn":"0373-3114","doi":"10.1007/s10231-020-00950-1"},"note":"","number":"5","number-of-pages":"36","page":"1923--1959","page-first":"1923","publisher":"","publisher-place":"","status":"","title":"Stratified periodic water waves with singular density gradients","type":"article-journal","username":"elkepeter","version":"","volume":"199"},"42d1b78569ecd89f80f0f48af825ce75mhartmann":{"DOI":"10.1002/zamm.201200141","ISBN":"","ISSN":"1521-4001","URL":"http://dx.doi.org/10.1002/zamm.201200141","abstract":"We consider conservation laws with spatially discontinuous flux that\n\tare perturbed by diffusion and dispersion terms. These equations\n\tarise in a theory of two-phase flow in porous media that includes\n\trate-dependent (dynamic) capillary pressure and spatial heterogeneities.\n\tWe investigate the singular limit as the diffusion and dispersion\n\tparameters tend to zero, showing strong convergence towards a weak\n\tsolution of the limit conservation law.","annote":"","author":[{"family":"Kissling","given":"F."},{"family":"Karlsen","given":"K.H."}],"citation-label":"kissling2013singular","collection-editor":[],"collection-title":"","container-author":[],"container-title":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift\n\tfür Angewandte Mathematik und Mechanik","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2013"]],"literal":"2013"},"event-place":"","id":"42d1b78569ecd89f80f0f48af825ce75mhartmann","interhash":"dfd390454fe4506ee81abb066cb2a4d4","intrahash":"42d1b78569ecd89f80f0f48af825ce75","issue":"","issued":{"date-parts":[["2013"]],"literal":"2013"},"keyword":"in Conservation porous function, capillarity, limit, media. flux singular law, dynamic discontinuous vorlaeufig flow two-phase","misc":{"issn":"1521-4001","doi":"10.1002/zamm.201200141"},"note":"","number":"","page":"n/a--n/a","page-first":"","publisher":"WILEY-VCH Verlag","publisher-place":"","status":"","title":"On the singular limit of a two-phase flow equation with heterogeneities\n\tand dynamic capillary pressure","type":"article-journal","username":"mhartmann","version":"","volume":""},"504fc9cccbcc450523cb5d98dd60a126hermann":{"DOI":"10.1007/s10614-015-9502-y","ISBN":"","ISSN":"0927-7099","URL":"","abstract":"In this paper the solutions to several variants of the so-called\n   dividend-distribution problem in a multi-dimensional, diffusion setting\n   are studied. In a nutshell, the manager of a firm must balance the\n   retention of earnings (so as to ward off bankruptcy and earn interest)\n   and the distribution of dividends (so as to please the shareholders). A\n   dynamic-programming approach is used, where the state variables are the\n   current levels of cash reserves and of the stochastic short-rate, as\n   well as time. This results in a family of Hamilton-Jacobi-Bellman\n   variational inequalities whose solutions must be approximated\n   numerically. To do so, a finite element approximation and a\n   time-marching scheme are employed.","annote":"","author":[{"family":"Barth","given":"Andrea"},{"family":"Moreno-Bromberg","given":"Santiago"},{"family":"Reichmann","given":"Oleg"}],"citation-label":"ISI:000371796600006","collection-editor":[],"collection-title":"","container-author":[],"container-title":"COMPUTATIONAL ECONOMICS","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["{2016}","MAR"]],"literal":"{2016}"},"event-place":"VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS","id":"504fc9cccbcc450523cb5d98dd60a126hermann","interhash":"ff9e17455504f09babc5aa7b043ed09e","intrahash":"504fc9cccbcc450523cb5d98dd60a126","issue":"3","issued":{"date-parts":[["{2016}","MAR"]],"literal":"{2016}"},"keyword":"Finite methods control; for Numerical differential method} Singular equations; distribution; stochastic element {Dividend partial","misc":{"author-email":"{andrea.barth@mathematik.uni-stuttgart.de\n   santiago.moreno@bf.uzh.ch\n   oleg.reichmann@math.ethz.ch}","issn":"{0927-7099}","keywords-plus":"{SEMIMARTINGALE; VOLATILITY; AMERICAN; POLICIES; OPTION; RISK}","funding-acknowledgement":"{ERC {[}AdG 247277, 249415-RMAC]; NCCR FinRisk (Project ``Banking and\n   Regulation{''}); Swiss Finance Institute (Project ``Systemic Risk and\n   Dynamic Contract Theory{''}); SNF {[}144130]; German Research Foundation\n   (DFG) as part of the Cluster of Excellence in Simulation Technology at\n   the University of Stuttgart {[}EXC 310/2]}","research-areas":"{Business \\& Economics; Mathematics}","eissn":"{1572-9974}","number-of-cited-references":"{34}","affiliation":"{Moreno-Bromberg, S (Reprint Author), Univ Zurich, Dept Banking \\& Finance, Plattenstr 32, CH-8032 Zurich, Switzerland.\n   Barth, Andrea, ETH, Dept Math, Seminar Appl Math, Ramistr 101, CH-8092 Zurich, Switzerland.\n   Barth, Andrea, Univ Stuttgart, SimTech, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany.\n   Moreno-Bromberg, Santiago, Univ Zurich, Dept Banking \\& Finance, Plattenstr 32, CH-8032 Zurich, Switzerland.\n   Reichmann, Oleg, ETH, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland.}","web-of-science-categories":"{Economics; Management; Mathematics, Interdisciplinary Applications}","language":"{English}","funding-text":"{We would like to thank the editor and an anonymous referee for their\n   comments and suggestions, which allowed us to improve our original\n   manuscript. It goes without saying that we assume full responsibility\n   for any remaining mistakes. The research leading to these results has\n   received funding form the ERC (Grant agreements AdG 247277 and\n   249415-RMAC), from NCCR FinRisk (Project ``Banking and Regulation{''}),\n   from the Swiss Finance Institute (Project ``Systemic Risk and Dynamic\n   Contract Theory{''}), from the SNF (Grant 144130) and from the German\n   Research Foundation (DFG) as part of the Cluster of Excellence in\n   Simulation Technology (EXC 310/2) at the University of Stuttgart, and it\n   is gratefully acknowledged.}","times-cited":"{0}","doi":"{10.1007/s10614-015-9502-y}"},"note":"","number":"3","number-of-pages":"25","page":"447-472","page-first":"447","publisher":"SPRINGER","publisher-place":"VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS","status":"","title":"A Non-stationary Model of Dividend Distribution in a Stochastic\n   Interest-Rate Setting","type":"article-journal","username":"hermann","version":"","volume":"47"}}