Abstract
We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on $ [a, +\infty), \ a>0 $). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.
Highlights
We wish to understand which effect the water-triggered microswelling of pores can have at observable scales of concrete-based materials
The main result of this paper is concerned with the existence and uniqueness of a locally in time solution in the sense of Definition 2.1 to the problem (P)u0,s0,h
In the proof of the existence of solutions, we use the abstract theory of evolution equations in Hilbert spaces governed by time-dependent subdifferentials which is characterized by the following form: ut(t) + ∂φt(u(t)) l(t) in H for t ∈ [0, T ], where φt is a proper, lower semi-continuous, convex function on Hilbert spaces H for t ∈ [0, T ], and ∂φt is the subdifferential of φt defined by
Summary
We wish to understand which effect the water-triggered microswelling of pores can have at observable scales of concrete-based materials. It is not at all clear how the sharp interface behaves close to corners, e.g. The paper is organized as follows: In Section 2, we state the used notation and assumptions as well as our main theorem concerning the existence and uniqueness of a solution for the moving boundary problem.
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