Efficient solution of a wave equation with fractional-order dissipative terms

In this paper, we study the traveling wave solutions of Allen–Cahn equation with a fractional Laplacian, where the nonlinear reaction is a bistable potential.. If the front of

The solutions obtained in the work are absent in the known reference manuals on differential equations, and the results obtained for continuously-heterogeneous anisotropic media

Then we show that the optimal control problem has also a unique solution that we characterize by means of first order Euler-Lagrange optimality condition and adjoint state which

We study an optimal control problem associated to a fractional wave equation involving Riemann-Liouville fractional derivative and with incomplete data. Actually, the initial

Key Words and Phrases: transport equation, fractional Brownian motion, Malliavin calculus, method of characteristics, existence and estimates of the density.. ∗ Supported by

Keywords and phrases: stochastic wave equation, random field solution, spa- tially homogenous Gaussian noise, fractional Brownian motion..

One of possible ways to understand the interaction between the anomalous diffusion operator (given by Λ α or, more generally, by the L´evy diffusion operator) and the nonlinearity

We will also study global existence, Besov regularity for weak solutions and a maximum principle and we will apply these results to the critical dissipative quasi-geostrophic