Related papers: A Class of Initial-Boundary Value Problems Governe…
We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy…
The global existence of strong solution to the initial-boundary value problem of the three-dimensional compressible viscoelastic fluids near equilibrium is established in a bounded domain. Uniform estimates in $W^{1,q}$ with $q>3$ on the…
We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…
This article is a continuation of earlier work [R.L. Huang and Y.H. Ye, On the second boundary value problem for a class of fully nonlinear flows I, to appear in International Mathematics Research Notices], where the long time existence and…
In this paper, we consider the initial boundary value problem for a pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. We use the potential well method to give a threshold result of global existence and finite-time blow-up…
We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal…
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases set in some bounded interval with boundary conditions prescribing the density of particles entering the…
In a continuum model of the solvation of charged molecules in an aqueous solvent, the classical Poisson-Boltzmann (PB) theory is generalized to include the solute point charges and the dielectric boundary that separates the high-dielectric…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
Our aim is to study the Total Variation Flow in Metric Graphs. First, we define the functions of bounded variation in Metric Graphs and their total variation, we also give an integration by parts formula. We prove existence and uniqueness…
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. We show that there exists a class of initial velocities such that the solution of the corresponding initial value problem exists only…
The overcoming of a mechanics problem on origin of secondary jet flows, on dynamics of its development and interaction with the main stream of the viscous fluid is reached by means of elucidation of the energy distribution in the stream at…
We derive conditions for the propagation of monotone ordering properties for a class of nonlinear parabolic partial differential equation (PDE) systems on metric graphs. For such systems, PDE equations with a general nonlinear dissipation…
In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Two theorems on strong solvability and the…
This paper deals with the initial-boundary value problem to a nonlocal semilinear pseudo-parabolic equation with conical degeneration, which has been studied in [Global well-posedness for a nonlocal semilinear pseudo-parabolic equation with…
We analyse the self-diffusiophoresis of a spherical particle animated by a nonuniform chemical reaction at its boundary. We consider two models of solute absorption, one with a specified distribution of interfacial solute flux, and one…
We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain $D$. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the…
We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit…
We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…