Well-posedness of the Fourier problem for higher-order weakly nonlinear integro-differential elliptic-parabolic equations

Well-posedness and asymptotics of some nonlinear integro-differential equations

We will prove the well-posedness of certain second order ordinary and partial integro-differential equations with an integral term of the form t ∫ 0 m(φ(t−s))φ̇(s) ds, wherem is given and φ is the solution. The new aspect is the dependence of the kernel on the solution. In addition, for the ordinary integro-differential equation, the asymptotic behaviour of the solution is described for some ker...

On the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations

for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained.

Well-posedness Results for Triply Nonlinear Degenerate Parabolic Equations

We study the well-posedness of triply nonlinear degenerate ellipticparabolic-hyperbolic problem b(u)t − div ã(u, ∇φ(u)) + ψ(u) = f, u|t=0 = u0 in a bounded domain with homogeneous Dirichlet boundary conditions. The nonlinearities b, φ and ψ are supposed to be continuous non-decreasing, and the nonlinearity ã falls within the Leray-Lions framework. Some restrictions are imposed on the dependence...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...