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We find steady channel flows that are locally optimal for transferring heat from fixed-temperature walls, under the constraint of a fixed rate of viscous dissipation (enstrophy = $Pe^2$), also the power needed to pump the fluid through the…
In this paper we study the Cauchy problem for new classes of parabolic type pseudodifferential equations over the rings of finite adeles and adeles. We show that the adelic topology is metrizable and give an explicit metric. We find…
We analyze the stability of a planar solid-solid interface at which a chemical reaction occurs. Examples include oxidation, nitridation, or silicide formation. Using a continuum model, including a general formula for the stress-dependence…
A finite element method of any order is applied on a Bakhvalov-type mesh to solve a singularly perturbed convection--diffusion equation in 2D, whose solution exhibits exponential boundary layers. A uniform convergence of (almost) optimal…
We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate…
In this work, we study the co-dimensional one interface limit and geometric motions of parabolic Ginzburg--Landau systems with potentials of high-dimensional wells. The main result generalizes the one by Lin et al. (Comm. Pure Appl. Math.,…
We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond…
We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…
A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity…
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
This paper establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the…
Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However its microscopic understanding still remains challenging. Here we…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
Although ubiquitous in nature and industrial processes, transport processes at the interface during evaporation and condensation are still poorly understood. Experiments have shown temperature discontinuities at the interface during…
We propose a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to…
A model combining Enskog's collision integral for dense fluids with a Vlasov-style description of the van der Waals force is applied to supercooling. First, the spinodal temperature $T_{s}$ is calculated, at which a liquid becomes unstable…