The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD) flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the flow. The equations governing the flow are modeled and then solved using the Laplace transform technique...

Solving parametric partial differential equations using artificial intelligence is taking the pace. It primarily because conventional numerical solvers are computationally expensive and require significant time to converge a solution. However, physics informed deep learning as an alternate learns functional spaces directly provides approximation reasonably fast compared solvers. The Fourier tra...

The probabilistic approach is used for constructing special layer methods to solve the Cauchy problem for semilinear parabolic equations with small parameter. In spite of the probabilistic nature these methods are nevertheless deterministic. The algorithms are tested by simulating the Burgers equation with small viscosity and the generalized KPP-equation with a small parameter. 1991 Mathematics...

The problem of fully developped turbulence is to characterize the statistical properties of the velocity field of a stirred fluid described by Navier stokes equations. The simplest scaling approach, due to Kolmogorov in 1941, gives a reasonable starting point, but it must be corrected due to the failure of naive scaling giving ‘intermittency’ corrections which are presumably associated with the...

Analytic continuation of viscous shock solution for the generalized Burgers equation with polynomial nonlinear source term is investigated. We show that a pertubated wave recovers its analyticity in the space variable in the strip limited by the first pair of conjugate poles of the wave.