相关论文: Global solutions to the supercooled Stefan problem…

When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational,…

This paper concerns the null controllability of the two-phase 1D Stefan problem with distributed controls. This is a free-boundary problem that models solidification or melting processes. In each phase, a parabolic equation, completed with…

We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…

In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…

We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational formulation of self-similar solutions, which allows to find…

A class of semi-bounded solutions of the two-dimensional incompressible Euler equations satisfying either periodic or Dirichlet boundary conditions is examined. For smooth initial data, new blowup criteria in terms of the initial concavity…

In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…

In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free…

We study the large-time behavior of solutions of a one-phase Stefan-type problem with anisotropic diffusion in periodic media on an exterior domain in a dimension $n \geq 3$. By a rescaling transformation that matches the expansion of the…

We investigate the regularizing behavior of two-phase Stefan problem near initial data. The main step in the analysis is to establish that in any given scale, the scaled solution is very close to a Lipschitz profile in space-time. We…

This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…

In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem \begin{align*} \left\{\begin{array}{ll}&-i u_t=\Delta u-V(x)u+f(x,|u|^2)u+(W\star|u|^2)u, \quad x\in\mathbb{R}^N, \quad t>0,…

In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems involving nonlinear partial differential equations, we provide several cautionary examples which indicate that modifications to the boundary…

We present a detailed numerical study of solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the $L^{2}$-subcritical case, numerical evidence is presented for the…

The main objective of this manuscript is to investigate the global behavior of the solutions to the viscoelastic wave equation with a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as a…

We study singularity formation for the focusing quadratic wave equation in the energy supercritical case, i.e., for $d \geq 7$. We find in closed form a new, non-trivial, radial, self-similar blowup solution $u^*$ which exists for all $d…

We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of $\sigma \to \sigma_0$ and $\delta \to\delta_0$, where…

We consider a class of ordinary differential equations in $d$-dimensions featuring a non-Lipschitz singularity at the origin. Solutions of such systems exist globally and are unique up until the first time they hit the origin, $t = t_b$,…

We consider the global existence and blow up of solutions of the Cauchy problem of the quasilinear wave equation: $\partial_{t}^2 u = \partial_x(c(u)^2 \partial_x u)$, which has richly physical backgrounds. Under the assumption that…

In microfluidic devices, droplets serving as carriers for chemical reactors or biomass can form stably encapsulated particles during the freezing process, holding significant importance in pharmaceuticals and microchemical reaction control.…