Multiple exact solutions for the dimensionally reduced p-gBKP equation via bilinear neural network method

In this paper, new trial functions are constructed via extended “3-3-2-3-1” and “3-3-2-3-2-1” network models based on the bilinear neural networks method. The new lump-type solution, interaction solution, plentiful arbitrary function solutions and periodic lump solutions of the dimensionally reduced [Formula: see text]-generalized Burgers–Kadomtsev–Petviashvili equation are solved. To analyze the dynamic properties of the solutions, appropriate parameters and different activated functions are defined in arbitrary function solutions. Through the three-dimensional and density plots, the dynamical characteristics of the solutions are shown well.

Computation of approximate solution to COVID-19 mathematical model

In this work, we investigate a modified population model of non-infected and infected (SI) compartmentsto predict the spread of the infectious disease COVID-19 in Pakistan. For Approximate solution, we use LaplaceAdomian Decomposition Method (LADM). With the help of the said technique, we develop an algorithmto compute series type solution to the proposed problem. We compute few terms approximate solutionscorresponding to different compartment. With the help of MATLAB, we also plot our approximate solutionsfor different compartment graphically.

On the Boundary Layer Equations with Phase Transition in the Kinetic Theory of Gases

Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in a half space. At the boundary of the half space, it is assumed that the gas is in contact with its condensed phase. The present paper discusses the existence and uniqueness of a uniformly decaying boundary layer type solution of the Boltzmann equation in this situation, in the vicinity of the Maxwellian equilibrium with zero bulk velocity, with the same temperature as that of the condensed phase, and whose pressure is the saturating vapor pressure at the temperature of the interface. This problem has been extensively studied, first by Sone, Aoki and their collaborators, by means of careful numerical simulations. See section 2 of (Bardos et al. in J Stat Phys 124:275–300, 2006) for a very detailed presentation of these works. More recently, Liu and Yu (Arch Ration Mech Anal 209:869–997, 2013) proposed an extensive mathematical strategy to handle the problems studied numerically by Sone, Aoki and their group. The present paper offers an alternative, possibly simpler proof of one of the results discussed in Liu and Yu (2013).

A saddle point type solution for a system of operator equations

Let Ω⊂Rn n>1 and let p,q≥2. We consider the system of nonlinear Dirichlet problems equation* brace(Au)(x)=Nu′(x,u(x),v(x)),x∈Ω,r-(Bv)(x)=Nv′(x,u(x),v(x)),x∈Ω,ru(x)=0,x∈∂Ω,rv(x)=0,x∈∂Ω,endequation* where N:R×R→R is C1 and is partially convex-concave and A:W01,p(Ω)→(W01,p(Ω))* B:W01,p(Ω)→(W01,p(Ω))* are monotone and potential operators. The solvability of this system is reached via the Ky–Fan minimax theorem.