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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

1 vote
0 answers
81 views

About the "method of lines": when are such solutions good approximations for **all** future ...

This question is about approximate solutions to some classes of PDEs obtained using the "method of lines". For example, for an initial-value problem given by a PDE on a circle, one can choose $n$ eq …
DC47's user avatar
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3 votes
0 answers
73 views

What is known about discrete versions of the spatially homogenous Boltzmann equation with fi...

Consider a discrete version of spatially homogenous Boltzmann equation with finitely many (but arbitrarily many) velocities $v_i \in \mathbb R^n$ with $i \in I$. Equivalently, consider a system of cou …
DC47's user avatar
  • 111