Related papers: Linear and Nonlinear Boundary Conditions: What's t…
We derive boundary conditions and estimates based on the energy and entropy analysis of systems of the nonlinear shallow water equations in two spatial dimensions. It is shown that the energy method provides more details, but is fully…
Linearisation is often used as a first step in the analysis of nonlinear initial boundary value problems. The linearisation procedure frequently results in a confusing contradiction where the nonlinear problem conserves energy and has an…
We present a straightforward energy stable weak implementation procedure of open boundary conditions for nonlinear initial boundary value problems. It simplifies previous work and its practical implementation.
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…
In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential…
In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…
We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy…
In this paper we consider an initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal Neumann boundary condition. We prove comparison principle, the existence theorem of a local solution and…
We discuss some recent developments in the theory of free boundary problems, as obtained in a series of papers in collaboration with L. Caffarelli, A. Karakhanyan and O. Savin. The main feature of these new free boundary problems is that…
In this paper, we deal with analysis of the initial-boundary value problems for the semilinear time-fractional diffusion equations, while the case of the linear equations was considered in the first part of the present work. These equations…