Related papers: Well-posedness for boundary value problems for coa…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
Existence of mass-conserving weak solutions to the coagulation-fragmentation equation is established when the fragmentation mechanism produces an infinite number of fragments after splitting. The coagulation kernel is assumed to increase at…
For a critical simple exchangeable fragmentation-coagulation process in slow regime where the coagulation rate and fragmentation rate are of the same order, we show that there exist phase transitions for its boundary behavior at infinity…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in…
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
In this paper, we study a class of initial-boundary value problems for the Korteweg-de Vries equation posed on a bounded domain $(0,L)$. We show that the initial-boundary value problem is locally well-posed in the classical Sobolev space…
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…
Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…
We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schr\"odinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
In this paper, we investigate the two-dimensional incompressible primitive equations with fractional horizontal dissipation. Specifically, we establish global well-posedness of strong solutions for arbitrarily large initial data when the…
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…
In this work we prove that the initial-boundary value problem (IBVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_t+\partial_x^5 u+u\partial_x u&\hspace{-2mm}=0,&\quad x\in\mathbb R^+,\;…
Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while…
This paper investigates an initial boundary value problem for the relaxed one-dimensional compressible Navier-Stokes-Fourier equations. By transforming the system into Lagrangian coordinates, the resulting formulation exhibits a uniform…
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…