Related papers: Stability analysis on the thermal insulation probl…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…
We study the quantitative transfer of uniqueness from the classical to the fractional Calder\'on problem with exterior data. This allows us to deduce the first stability estimates for the principal part of the isotropic fractional…
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as…
This paper is concerned with stability of the ball for a class of isoperimetric problems under convexity constraint. Considering the problem of minimizing $P+\varepsilon R$ among convex subsets of $\mathbb{R}^N$ of fixed volume, where $P$…
The global static stability of a Starling Resistor conveying non-Newtonian fluid is considered. The Starling Resistor consists of two rigid circular tubes and axisymmetric collapsible tube mounted between them. Upstream and downstream…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
The stability of a dilute plasma to local convective and rotational disturbances is examined. A subthermal magnetic field and finite thermal conductivity along the field lines are included in the analysis. Stability criteria similar in form…
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…
The problem of the stability of a nonlinear thermomagnetic wave with respect to small thermal and electromagnetic perturbations in hard superconductors was studied. It is shown that spatially bounded solutions may correspond only to the…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…
In the present paper, we study the boundary concentration breaking phenomena on two thermal insulation problems considered on Lipschitz domains, based on Serrin's overdetermined results, perturbation argument and comparison of Laplacian…
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…