A linear-implicit finite difference scheme is given for the initial-boundary problem of GBBMBurgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is effici...

We consider the initial-boundary value problem describing a complex (radiativeconductive) heat transfer in system of grey bodies with semitransparent inclusions. establish unique solvability this problem. prove comparison theorem and show that increasing integrability property data improves properties solutions, including exponential boundedness.

This paper is devoted to the study of a class evolution inclusion in Banach spaces with nonlocal plus local mixed initial conditions. Under some mild assumptions, unique solvability result multivalued problem obtained via arguments fixed point principle and theory $C^0$-semigroup.

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the earth’s surface. downward continuation is a...