Related papers: Global mild solutions for a transport-diffusion eq…
In this paper, we consider the following Dirichlet problem for the fully nonlinear elliptic equation of Grad-Mercier type under asymptotic convexity conditions \begin{equation*} \left\{ \begin{array}{ll} F(D^2u(x),Du(x),u(x),x)=g(|\{y\in…
We consider the Cauchy problem for the Hamilton-Jacobi equation with critical dissipation, $$ \partial_t u + (-\Delta)^{ 1/2} u = |\nabla u|^p, \quad x \in \mathbb R^N, t > 0, \qquad u(x,0) = u_0(x) , \quad x \in \mathbb R^N, $$ where $p >…
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error…
We prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an explicit counter-example that the linear growth condition is not…
In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
We provide an existence and uniqueness result for mild solutions to semilinear stochastic partial differential equations in the framework of the semigroup approach with locally monotone coefficients. An important component of the proof is…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
In this article an analytical solution of equations of motion of a rigid disk of finite thickness rolling on its edge on a perfectly rough horizontal plane under the action of gravity is given. The solution is given in terms of Gauss…
In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…
In this paper we establish the uniqueness of a solution to a stationary convection-diffusion equation in divergence form with an exponentially summable generalized divergence-free drift.
In this paper, we establish the uniquely existence of the global mild solution to the nematic liquid crystal equations in Besov-Morrey spaces. Some self-similarity and large time behavior of the global mild solution are also investigated.
A system of drift-diffusion equations with electric field under Dirichlet boundary conditions is analyzed. The system of strongly coupled parabolic equations for particle density and spin density vector describes the spin-polarized…
We give sufficient conditions for global existence of positive mild solutions for the weak coupled system: \begin{eqnarray*} \frac{\partial u_{1}}{\partial t}…
In this paper, we are concerned with the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping \begin{equation*} \partial_t\rho+\operatorname{div}(\rho u)=0, \quad…
Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a…
Neutral particles in the plasma edge of fusion devices based on magnetic confinement are described by a transient kinetic equation incorporating ionization, recombination, and charge-exchange collisions. In charge-exchange dominated…
Many steady-state transport problems in condensed matter physics can be reduced to a set of coupled diffusion equations. This is true in particular when relaxation processes are sufficiently fast that the system is in the diffusive…
Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…
Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime,…