Abstract. In this article, second order numerical methods for optimal control of the monodomain equations in cardiac electrophysiology are presented. The monoand bidomain equations are well established as a major building block for describing the the wave propagation of the action potential in the human heart. The mathematical model equations consist of a non-linear parabolic partial differenti...

in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. ...

We establish weighted L2-estimates for the wave equation with variable damping utt −∆u+ aut = 0 in R, where a(x) ≥ a0(1+ |x|)−α with a0 > 0 and α ∈ [0, 1). In particular, we show that the energy of solutions decays at a polynomial rate t−(n−α)/(2−α)−1 if a(x) ∼ a0|x|−α for large |x|. We derive these results by strengthening significantly the multiplier method. This approach can be adapted to ot...

In this article we consider variable coefficient, time dependent wave equations in exterior domains R × (R \ Ω), n ≥ 3. We prove localized energy estimates if Ω is star-shaped, and global in time Strichartz estimates if Ω is strictly convex.

We establish weighted L2−estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the L2−norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is developed. The complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable φ=φp − φe representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are o...