<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">OALibJ</journal-id><journal-title-group><journal-title>Open Access Library Journal</journal-title></journal-title-group><issn pub-type="epub">2333-9705</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/oalib.1104155</article-id><article-id pub-id-type="publisher-id">OALibJ-81164</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Biomedical&amp;Life Sciences</subject><subject> Business&amp;Economics</subject><subject> Chemistry&amp;Materials Science</subject><subject> Computer Science&amp;Communications</subject><subject> Earth&amp;Environmental Sciences</subject><subject> Engineering</subject><subject> Medicine&amp;Healthcare</subject><subject> Physics&amp;Mathematics</subject><subject> Social Sciences&amp;Humanities</subject></subj-group></article-categories><title-group><article-title>
 
 
  On the Solvability of the Boundary-Value Problem for the First Order Operator-Differential Equations with Multiple Characteristics
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mohamed</surname><given-names>A. Labeeb</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ahmed</surname><given-names>L. Elbably</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Abdel</surname><given-names>Baset I. Ahmed</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib></contrib-group><aff id="aff2"><addr-line>Helwan University, Helwan, Egypt</addr-line></aff><aff id="aff1"><addr-line>Egyptian Russian University, Badr City, Egypt</addr-line></aff><pub-date pub-type="epub"><day>01</day><month>12</month><year>2017</year></pub-date><volume>04</volume><issue>12</issue><fpage>1</fpage><lpage>4</lpage><history><date date-type="received"><day>15,</day>	<month>November</month>	<year>2017</year></date><date date-type="rev-recd"><day>16,</day>	<month>December</month>	<year>2017</year>	</date><date date-type="accepted"><day>19,</day>	<month>December</month>	<year>2017</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  In this pa
  per, a class of operator-differential equation of the first order with multiple characteristics is considered, for which the initial boundary value problem on the semi-axis is well-posed and uniquely solvable in the Sobolev space.
 
</p></abstract><kwd-group><kwd>Operator-Differential Equation</kwd><kwd> Boundary-Value Problem</kwd><kwd> Hilbert Space</kwd><kwd> Reg-ular Solvability</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>Cite this paper</title><p>Labeeb, M.A., Elbably, A.L. and Ahmed, A.B.I. (2017) On the Solvability of the Boundary-Value Pro- blem for the First Order Operator-Dif- ferential Equations with Multiple Charac- teristics. Open Access Library Journal, 4: e4155. https://doi.org/10.4236/oalib.1104155</p></sec></body><back><ref-list><title>References</title><ref id="scirp.81164-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Hille, E. and Fillips, R.S. (1957) Functional Analysis and Semi-Groups. Amer. Math. Soc. Coll. Publ., Vol. 31, Amer. Math. Soc., Providence, 1957; Izdat. Inostran. Lit., Moscow, 1962.</mixed-citation></ref><ref id="scirp.81164-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Lions, J.-L. and Magenes, E. Non-Homogeneous Boundary Value Problems and Applications. Dunod, Paris, 1968; Mir, Moscow, 1971; Springer, Berlin, 1972.</mixed-citation></ref><ref id="scirp.81164-ref3"><label>3</label><mixed-citation publication-type="other" xlink:type="simple">Amann, H. (2005) Maximal Regularity and Quasilinear Parabolic Boundary Value Problems, Recent Advances in Elliptic and Parabolic Problems. World Scientific, Hack-ensack, 1-17.</mixed-citation></ref><ref id="scirp.81164-ref4"><label>4</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Sasun Yakubov</surname><given-names> U. </given-names></name>,<etal>et al</etal>. (<year>1999</year>)<article-title>An Initial Boundary Value Problem for Parabolic Differential-Operator Equations</article-title><source> Journal of Mathematical Analysis and Applications</source><volume> 239</volume>,<fpage> 272</fpage>-<lpage>290</lpage>.<pub-id pub-id-type="doi"></pub-id></mixed-citation></ref><ref id="scirp.81164-ref5"><label>5</label><mixed-citation publication-type="other" xlink:type="simple">Yakubov, S.Ya. (1985) Linear Differential-Operator Equations and Their Applications. Elm, Baku. (In Russian)</mixed-citation></ref></ref-list></back></article>