In this paper, we discuss the Landau-Lifshitz equations with applied magnetic fields. The equations describing the bubbles in the ferromagnets and the behaviors of the solutions near the singularities are given. We found that the applied fields do not affect the bubbles and we have the same conclusions as in reference [1].

We study the structure and behavior of non-negative radial solution for the following elliptic equation Δu = u^ν, x ∈ \mathbb{R}^n with 0 < ν < 1. We also obtain the detailed asymptotic expansion of u near infinity.

We prove the existence, uniqueness and finite propagation of disturbance of continuous solutions to the Cauchy problem for one-dimensional p-Laplacian equation with point source.

The aim of this paper is to discuss the existence and uniqueness of solutions for the porous medium equation u_t - (u^m)_{xx} = μ(x) in (x, t) ∈ \mathbb{R} × (0, +∞) with initial condition u(x, 0) = u_0(x) x ∈ (-∞, +∞), where μ(x) is a nonnegative finite Radon measure, u_0 ∈ L¹(\mathbb{R}) ∩ L∞(\mathbb{R}) is a nonnegative function, and m > 1, and \mathbb{R} ≡ (-∞, +∞).