Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Energetic Variational Approach for the Cahn--Hilliard Equation with
  Dynamic Boundary Condition: Model Derivation and Mathematical Analysis   The Cahn--Hilliard equation is a fundamental model that describes phase
separation processes of binary mixtures. In recent years, several types of
dynamic boundary conditions have been proposed in order to account for possible
short-range interactions of the material with the solid wall. Our first aim in
this paper is to propose a new class of dynamic boundary conditions for the
Cahn--Hilliard equation in a rather general setting. The derivation is based on
an energetic variational approach that combines the least action principle and
Onsager's principle of maximum energy dissipation. One feature of our model is
that it naturally fulfills three important physical constraints such as
conservation of mass, dissipation of energy and force balance relations. Next,
we provide a comprehensive analysis of the resulting system of partial
differential equations. Under suitable assumptions, we prove the existence and
uniqueness of global weak/strong solutions to the initial boundary value
problem with or without surface diffusion. Furthermore, we establish the
uniqueness of asymptotic limit as $t\to+\infty$ and characterize the stability
of local energy minimizers for the system.

35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th