<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:METS="http://www.loc.gov/METS/" xmlns:fits="http://hul.harvard.edu/ois/xml/ns/fits/fits_output" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:IR="http://dl.lib.brown.edu/md/irdata" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:rights="http://cosimo.stanford.edu/sdr/metsrights/" ID="etd348">
     <mods:titleInfo>
      <mods:title>Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs</mods:title>
     </mods:titleInfo>
     <mods:name type="personal">
      <mods:namePart>Ben-Gal, Nitsan</mods:namePart>
      <mods:role>
       <mods:roleTerm type="text">creator</mods:roleTerm>
      </mods:role>
     </mods:name>
     <mods:originInfo>
      <mods:copyrightDate keyDate="yes" encoding="w3cdtf">2009</mods:copyrightDate>
     </mods:originInfo>
     <mods:physicalDescription>
      <mods:extent>xvi, 187 p.</mods:extent>
      <mods:digitalOrigin>born digital</mods:digitalOrigin>
     </mods:physicalDescription>
     <mods:note>Thesis (Ph.D.) -- Brown University (2009)</mods:note>
     <mods:name type="personal">
      <mods:namePart>Fieldler, Bernold</mods:namePart>
      <mods:role>
       <mods:roleTerm type="text">director</mods:roleTerm>
      </mods:role>
     </mods:name>
     <mods:name type="personal">
      <mods:namePart>Dafermos, Constantine</mods:namePart>
      <mods:role>
       <mods:roleTerm type="text">reader</mods:roleTerm>
      </mods:role>
     </mods:name>
     <mods:name type="personal">
      <mods:namePart>Sandstede, Bjorn</mods:namePart>
      <mods:role>
       <mods:roleTerm type="text">reader</mods:roleTerm>
      </mods:role>
     </mods:name>
     <mods:name type="corporate">
      <mods:namePart>Brown University. Applied Mathematics</mods:namePart>
      <mods:role>
       <mods:roleTerm type="text">sponsor</mods:roleTerm>
      </mods:role>
     </mods:name>
     <mods:genre authority="aat">theses</mods:genre>
     <mods:abstract>In recent years, there has been a great deal of interest surrounding the study of the asymptotics and global attractor structure for scalar parabolic PDEs which are either
      dissipative or undergo finite-time blow-up. This thesis presents solutions to the asymptotics and connection problems for slowly non-dissipative scalar PDEs, i.e. the final remaining class of
      scalar parabolic reaction-diffusion equations. Such PDEs produce solutions that neither blow up nor are dissipative. These "grow-up" solutions grow to infinite norm in infinite time, and it is
      the added challenges they introduce that are overcome in this thesis. In the pursuit of this result, a number of new concepts are defined, including slowly non-dissipative PDEs, non-compact
      global attractors, and the completed inertial manifold. Many of the underlying assumptions used in the study of dissipative PDEs are inapplicable to slowly non-dissipative PDEs. Thus, concepts
      must be redefined and techniques updated or extended. The effects of a slowly non-dissipative nonlinearity on the global bifurcation diagram are investigated, and the y-map, a technique critical
      to solving the connection problem for dissipative systems, is extended to slowly non-dissipative PDEs and a wider range of boundary conditions. The completed inertial manifold is introduced and
      proven to exist for certain classes of slowly non-dissipative equations. The development of this new structure and its advantageous characteristics provide the tools necessary to prove
      convergence for grow-up solutions which form heteroclinic connections to infinity. The asymptotics of grow-up solutions are determined, and via combining the various expanded techniques, a full
      decomposition of the non-compact global attractor is produced for a generic choice of nonlinearity. The results are studied for a selection of interesting cases and are shown to hold for both
      Neumann and Dirichlet boundary conditions.</mods:abstract>
     <mods:subject authority="local">
      <mods:topic>grow-up</mods:topic>
     </mods:subject>
     <mods:subject authority="local">
      <mods:topic>global attractor</mods:topic>
     </mods:subject>
     <mods:subject authority="local">
      <mods:topic>semilinear parabolic PDE</mods:topic>
     </mods:subject>
     <mods:subject authority="local">
      <mods:topic>asymptotic behavior</mods:topic>
     </mods:subject>
     <mods:subject authority="local">
      <mods:topic>connecting orbits</mods:topic>
     </mods:subject>
     <mods:subject authority="local">
      <mods:topic>inertial manifold</mods:topic>
     </mods:subject>
     <mods:recordInfo>
      <mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource>
      <mods:recordCreationDate encoding="iso8601">20091218</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:identifier type="doi">10.7301/Z0MW2FFK</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>