On the generalized Burgers-Huxley equation: Existence, uniqueness, regularity, global attractors and numerical studies

In this work, we consider the forced generalized Burgers-Huxley equation and establish existence uniqueness of a global weak solution using Faedo-Galerkin approximation method. Under smoothness assumptions on initial data external forcing, also obtain further regularity results solutions. Taking forcing to be zero, positivity result as well bound classical are established. Furthermore, examine long-term behavior solutions equations. We first absorbing balls in appropriate spaces for semigroup associated with then show attractor system. The inviscid limits equations Burgers Huxley discussed. Next, stationary by technique compactness arguments. Then, discuss about exponential stability Concerning numerical studies, derive error estimates semidiscrete Galerkin approximation. Finally, present two computational examples convergence numerically.