Let (Ω,A, P ) be a complete probability space. We show that the trivial function is the unique L-solution of the following refinement type equation f(x) = Z Ω |φx(x, ω)|f(φ(x, ω))dP (ω) for a wide class of the given functions φ. This class contains functions of the form φ(x, ω) = α(ω)x−β(ω) with −∞ < R Ω log |α(ω)|dP (ω) < 0.

The Hunter–Saxton equation and the Gurevich–Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions are obtained exactly.

In this paper we study the dynamics of a Burgers’ type equation (1.1). First, we use a new method called attractor bifurcation introduced by Ma and Wang in [4, 6] to study the bifurcation of Burgers’ type equation out of the trivial solution. For Dirichlet boundary condition, we get pitchfork attractor bifurcation as the parameter λ crosses the first eigenvalue. For periodic boundary condition,...

Subdiffusion in a system in which mobile particles A can chemically react with static particles B according to the rule A+B→B is considered within a persistent random-walk model. This model, which assumes a correlation between successive steps of particles, provides hyperbolic Cattaneo normal diffusion or fractional subdiffusion equations. Starting with the difference equation, which describes ...

The goal of this work is to look at how heat transfer affects the oscillating flow a hydrodynamically magnetizing Prandtl-Eyring fluid through porous material under impact temperature and concentration two different engineering conditions: Poiseuille Couette flow. To get an unambiguous formula for motion, we utilized perturbation approach. Graphs are used illustrate findings..

in the present paper an operator-differential equation of second order in complex domain isconsidered when the coefficients have singularity of pole type at the point z=0. a theorem of existence of thesolution of the equation is proved and the spectral property of the solution is separately investigated when thecoefficients are spectral operators.

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

In this paper we find a certain solution of Poisson type fractional differential equation using theory tensor product Banach spaces.