Abstract Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky systems. The order $$\alpha $$ α the Caputo derivative belongs interval (1, 2). We achieve such suitable class weak solutions.

Two-level additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar second-order symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergence-free nonconforming P1 finite element approximation of the stationary Stokes equations. The condition numbers of th...

We prove the decay in energy space for solution to defocusing biharmonic Hartree-Fock equations with mass-supercritical and energy-subcritical Choquard-type nonlinearity dimension d⩾3. treat both free perturbed by a potential case. As direct consequence, we obtain large-data scattering H2(Rd)N,N⩾1.

This paper makes a short study of Fredholm integral equations related to potential theory and elasticity, with a view to preparing the ground for their exploitation in the numerical solution of difficult boundary-value problems. Attention is drawn to the advantages of Fredholm's first equation and of Green's boundary formula. The latter plays a fundamental and hitherto unrecognized role in the ...

fies the biharmonic equation. The detailed behavior of solutions to the biharmonic equation on regions with corners has been historically difficult to characterize. The problem was first examined by Lord Rayleigh in 1920; in 1973, the existence of infinite oscillations in the domain Green’s function was proven in the case of the right angle by S. Osher. In this paper, we observe that, when the ...

We numerically simulate the following two nonlinear evolution equations with a fourth order (biharmonic) leading term: −∆2u− 1 22 (|u|2 − 1)u = ut in Ω ⊂ R or R and −∆2u + 1 22 ∇ · ((|∇u|2 − 1)∇u) = ut in Ω ⊂ R or R with an initial value and a Dirichlet boundary conditions. We use a bivariate spline space like finite element method to solve these equations. We discuss the convergence of our num...

We have used the multiquadric (MQ) approximation scheme for the solution of elliptic partial differential equations with Dirichlet and/or Neumann boundary conditions. The scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering. Two-dimensional Laplace, Poisson, and biharmonic equations describing the various physical processes have been taken as the t...

Solving boundary value problems BVPs for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation,...