Parabolic systems and an underlying Lagrangian

Show simple item record Yolcu, Türkay en_US 2009-08-26T18:17:03Z 2009-08-26T18:17:03Z 2009-07-07 en_US
dc.description.abstract In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L¹. en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Lagrangian en_US
dc.subject PDE en_US
dc.subject Parabolic equations en_US
dc.subject Variational method en_US
dc.subject De Giorgi en_US
dc.subject Optimization en_US
dc.subject.lcsh Differential equations, Parabolic
dc.subject.lcsh Lagrangian functions
dc.subject.lcsh Interpolation
dc.subject.lcsh Algorithms
dc.title Parabolic systems and an underlying Lagrangian en_US
dc.type Dissertation en_US Ph.D. en_US
dc.contributor.department Mathematics en_US
dc.description.advisor Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph en_US

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