Self-similar solutions in a sector for a quasilinear parabolic equation

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Asymptotic Self - Similar Global Blow - Upfor a Quasilinear Heat

We study the asymptotic behaviour near nite blow-up time t = T of the solutions to the one-dimensional degenerate quasilinear parabolic equation u t = (u u x) x + u in R (0; T); > 0; 1 < < + 1; with bounded, nonnegative, compactly supported initial data. This parameter range corresponds to global blow-up where u(x; t) ! 1 as t ! T ? for any x 2 R. We prove that the rescaled function f(; t) = (T...

Quasilinear Schrödinger equations involving critical exponents in $mathbb{textbf{R}}^2$

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Blow-up Behavior for a Quasilinear Parabolic Equation with Nonlinear Boundary Condition

In this paper, we study the solution of an initial boundary value problem for a quasilinear parabolic equation with a nonlinear boundary condition. We first show that any positive solution blows up in finite time. For a monotone solution, we have either the single blow-up point on the boundary, or blow-up on the whole domain, depending on the parameter range. Then, in the single blow-up point c...