Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 4 of 4 for “"Analysis of PDEs"”.
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Stable and Unstable Shock Formation of the Burgers-Hilbert Equation
The study of singularities has been an important part in the analysis of PDEs. One key type of singularities is shock. In many cases the shock has a self-similarity structure. Recently, the modulated self-similarity technique has achieved success in fluid dynamic equations. In this thesis, we apply …
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On the derivation of non-local diffusion equations in confined spaces
The subject of the thesis is the derivation of non-local diffusion equations from kinetic models with heavy-tailed equilibrium in velocity. We are particularly interested in confining the kinetic equations and developing methods that allow us, from the confined kinetic models, to derive confined …
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The broken non-abelian X-ray transform and inverse problems for connections at high fixed frequency
This thesis is concerned with the recovery of a u(n) -valued connection A on a Hermitian vector bundle E of rank n over a smooth Riemannian or Lorentzian manifold with boundary (M, g) from different geometric inverse problems. The connection is to be recovered up to a gauge that is the identity on …
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The Calderón problem for connections
This thesis is concerned with the inverse problem of determining a unitary connection $A$ on a Hermitian vector bundle $E$ of rank $m$ over a compact Riemannian manifold $(M, g)$ from the Dirichlet-to-Neumann (DN) map $\Lambda_A$ of the associated connection Laplacian $d_A^*d_A$. The connection is …