Related papers: A Class of Initial-Boundary Value Problems Governe…
We prove universality of a macroscopic behavior of solutions of a large class of semi-linear parabolic SPDEs on $\mathbb{R}_+\times\mathbb{T}$ with fractional Laplacian $(-\Delta)^{\sigma/2}$, additive noise and polynomial non-linearity,…
We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…
End-point maximal $L^1$-regularity for parabolic initial-boundary value problems is considered. For the inhomogeneous Dirichlet and Neumann data, maximal $L^1$-regularity for initial-boundary value problems is established in time end-point…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…
Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including definition of a solution, explicit examples and the notion of…
We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The…
We consider the unsteady problem for the general planar Broadwell model with four velocities in a rectangular spatial domain over a finite time interval. We impose a class of non-negative initial and Dirichlet boundary data that are bounded…
We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in channel-like domains on a time interval $(0,T)$. For the parabolic system with strong nonlinearities and including the…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a reaction diffusion equation with special diffusion processes. It is shown, under certain conditions on the initial data, that the…
We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics.…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space.…
We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption that the fields are bounded. In the case…