Related papers: Free boundary problem governed by a non-linear dif…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…
In this paper we develop an existence theory for the nonlinear initial-boundary value problem with singular diffusion $\partial_t u = \text{div}(k(x)\nabla G(u))$, $u|_{t=0}=u_0$ with Neumann boundary conditions $k(x)\nabla G(u)\cdot \nu =…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar curve sliding along the boundary with a zero contact angle,…
We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the…
A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first…
In this paper, we consider a free boundary problem with a nonlocal diffusion kernel function $k(x)$. Due to the long distance exchange effect of nonlocal diffusion, the free boundary can expand discontinuously, which makes the problem…
A model of unsteady filtration (seepage) in a porous medium with capillary retention is considered. It leads to a free boundary problem for a generalized porous medium equation where the location of the boundary of the water mound is…
We consider self-similar approximations of nonlinear hyperbolic systems in one space dimension with Riemann initial data and general diffusion matrix. We assume that the matrix of the system is strictly hyperbolic and the diffusion matrix…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
Recently, we have proposed a new free boundary problem representing the bread baking process in a hot oven. Unknown functions in this problem are the position of the evaporation front, the temperature field and the water content. For…
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that…
In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…
This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…
We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…
We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\in}]c*,…