<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:METS="http://www.loc.gov/METS/" ID="etd636" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd">
          <mods:titleInfo>
            <mods:title>Initial Boundary Value Problem of the Boltzmann Equation</mods:title>
          </mods:titleInfo>
          <mods:name type="personal">
            <mods:namePart>Kim, Chanwoo </mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">creator</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:originInfo>
            <mods:copyrightDate>2011</mods:copyrightDate>
          </mods:originInfo>
          <mods:physicalDescription>
            <mods:extent>vii, 191 p.</mods:extent>
            <mods:digitalOrigin>born digital</mods:digitalOrigin>
          </mods:physicalDescription>
          <mods:note>Thesis (Ph.D. -- Brown University (2011)</mods:note>
          <mods:name type="personal">
            <mods:namePart>Guo, Yan</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Director</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="personal">
            <mods:namePart>Strauss, Walter</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Reader</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="personal">
            <mods:namePart>Holmer, Justin</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">Reader</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:name type="corporate">
            <mods:namePart>Brown University. Mathematics</mods:namePart>
            <mods:role>
              <mods:roleTerm type="text">sponsor</mods:roleTerm>
            </mods:role>
          </mods:name>
          <mods:genre authority="aat">theses</mods:genre>
          <mods:subject>
            <mods:topic>partial differential equation</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>Boltzmann equation</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>boundary condition</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>singularity</mods:topic>
          </mods:subject>
          <mods:subject>
            <mods:topic>large external potential</mods:topic>
          </mods:subject>
          <mods:subject authority="FAST" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/893484"><mods:topic>Differential equations, Partial</mods:topic></mods:subject><mods:recordInfo>
            <mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource>
            <mods:recordCreationDate encoding="iso8601">20111003</mods:recordCreationDate>
          </mods:recordInfo>
        <mods:language><mods:languageTerm type="code" authority="iso639-2b">eng</mods:languageTerm><mods:languageTerm type="text">English</mods:languageTerm></mods:language><mods:abstract>In this thesis, we study some boundary problems of the Boltzmann equation and the Boltzmann equation with the large external potential.If the gas is contained in a bounded domain or flows past a solid bodies, the Boltzmann equation must be accompanied by boundary conditions, which describe the interaction of the gas with the solid walls. The basic boundary conditions are in-flow injection, diffuse reflection, bounce-back, and specular reflection boundary conditions.First, we demonstrate that discontinuity of the Boltzmann solution is created at the non-convex part of the grazing boundary, then propagate only along the forward characteristics inside the domain before it hits on the boundary again with the in-flow injection, diffuse reflection and bounce-back boundary conditions. The main ingredient is the new regularizing effect of the gain term.Second, we prove the global well-posedness of the Boltzmann equation with the specular reflection boundary condition when the domain is the cylindrical shape. The main ingredients are introducing collision-pair map to show the transversality and developing the graph comparison method to characterize grazing velocities for the non-convex domains.If the gas particles are charged and there is background electonic potential, the Boltzmann equation is accompanied by the field term ∇χΦ⋅∇ᵥF in the equation. The global well-posedness in the presence of the large external potential is an important open problem. We use Asano's work, showing the transversality in the presence of potentials, in L&lt;sup&gt;p&lt;/sup&gt; - L&lt;sup&gt;∞&lt;/sup&gt; framework to resolve this problem.</mods:abstract><mods:identifier type="doi">10.7301/Z0XD0ZX8</mods:identifier><mods:accessCondition type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">Collection is open for research.</mods:accessCondition><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource></mods:mods>