in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

As is known, it customary in the literature to divide degenerate equations of mixed type into first and second kind. In case an equation kind, contrast first, degeneracy line simultaneously envelope a family characteristics, i.e. itself characteristic, which causes additional difficulties study boundary value problems for this paper, order establish unique solvability one nonlocal problem with ...

This paper shows the unique solvability of elliptic problems associated with two-phase incompressible flows, which are governed by Navier-Stokes equations a sharp moving interface, in unbounded domains such as whole space separated compact interface and non-compact interface. As by-product, we obtain Helmholtz-Weyl decomposition for flows.

We study a new mathematical model of locally nonequilibrium processes heat, mass, and momentum transfer taking into account the relaxation phenomena based on hyperbolic parabolic equations. also propose method aimed at getting priori Schauder-type estimates. The unique solvability problem with inner-boundary nonlocal conditions is established.

Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain guarding operations. On the other hand, many models of iteration do admit unguarded iteration. Solutions are then no longer unique, and in general not even de...

We establish sufficient conditions for the unique solvability of inverse problem finding two unknown functions from a Schwarz-type space smooth rapidly decreasing at infinity on right-hand side diffusion equation with Caputo–Djrbashian time fractional derivative. In this case, we use overdetermination integral respect to time.

Models of iterated computation, such as (completely) iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain guarding operations. On the other hand, many models of iteration do admit unguarded iteration. Solutions are then no longer unique, and in general not even de...

In this paper, a multipoint boundary value problem for systems of integro-differential equations with involution has been studied. To solve the studied problem, parameterization method is used. Based on parametrization method, decomposed into two parts, i.e., Cauchy and system linear equations. Necessary sufficient conditions unique solvability are determined.

Abstract We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that heat semigroup is ultracontractive we unique solvability non-empty subgraphs with respect to vertex boundary and provide analytic probabilistic representations solutions. A second result deals canonically compactifiable graphs Royden provides conditions representations.

1. Summary. In Part I, we develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and...