Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak solutions for multiquasilinear elliptic-parabolic systems.
  Application to thermoelectrochemical problems   This paper investigates the existence of weak solutions of biquasilinear
boundary value problem for a coupled elliptic-parabolic system of divergence
form with discontinuous leading coefficients. The mathematical framework
addressed in the article considers the presence of an additional nonlinearity
in the model which reflects the radiative thermal boundary effects in some
applications of interest. The results are obtained via the Rothe-Galerkin
method. Only weak assumptions are made on the data and the boundary conditions
are allowed to be on a general form. The major contribution of the current
paper is the explicit expressions for the constants appeared in the
quantitative estimates that are derived. These detailed and explicit estimates
may be useful for the study on nonlinear problems that appear in the real world
applications. In particular, they clarify the smallness conditions. In
conclusion, we illustrate how the above results may be applied to the
thermoelectrochemical phenomena in an electrolysis cell. This problem has
several applications as for instance to optimize the cell design and operating
conditions.

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th