A semigroup approach to functional differential evolution equations. (20th June 2013)

• Record Type: Journal Article
• Authors: Athanasiadou, Evagelia S.; Dionysatos, Vasileios F.; Koumantos, Panagiotis N.; Pavlakos, Panaiotis K.; Barbatis, Gerassimos; Stratis, Ioannis
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 2(2014:Jan. 30)
• Page Start: 217
• Page End: 222
• Publication Date: 2013-06-20
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2891
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2891-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2891-para-0001">We study functional differential evolution equations of the form <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4t701qmn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2891:mma2891-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced open="(" close=")"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mi>∂t</mml:mi></mml:mrow></mml:mfrac><mml:mo class="MathClass-bin">+</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:mfenced><mml:mi>x</mml:mi><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo class="MathClass-close">)</mml:mo></mml:mrow><mml:mo class="MathClass-rel">=</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo class="MathClass-punc">, </mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:math></alternatives>, where − <italic>A</italic> is infinitesimal generator of an analytic semigroup in a Banach space <italic>E</italic> (with or without order) and the given right‐hand side modelling delay. In many cases, <italic>E</italic> is a Banach space of sections, such as vector field or differential forms of a (real or complex) vector bundle <italic>Ω</italic> (of possibly infinite dimension) over a locally convex manifold, for example, a Carathéodory–Finsler manifold. The operator <italic>A</italic> may in particular be generated by a Dirichlet form acting on an ordered Hilbert space. As an application, we consider a problem from thermo‐magnetohydrodynamics. Copyright © 2013 John Wiley & Sons, Ltd.</p> </abstract>