Global solutions for a nonlinear hyperbolic equation with boundary memory source term

Existence and Uniform Decay of Solutions of a Parabolic-Hyperbolic Equation with Nonlinear Boundary Damping and Boundary Source Term

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Global Solutions and Blow-up Profiles for a Nonlinear Degenerate Parabolic Equation with Nonlocal Source

This paper deals with a degenerate parabolic equation vt = ∆v + av1 ∥v∥1 α1 subject to homogeneous Dirichlet condition. The local existence of a nonnegative weak solution is given. The blow-up and global existence conditions of nonnegative solutions are obtained. Moreover, we establish the precise blow-up rate estimates for all the blow-up solutions.

Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term

and Applied Analysis 3 Baeumer et al. 8, 13 have proved existence and uniqueness of a strong solution for 1.2 using the semigroup theory when f x, t, u is globally Lipschitz continuous. Furthermore, when f x, t, u is locally Lipschitz continuous, existence of a unique strong solution has also been shown by introducing the cut-off function. Finite difference methods have been studied in 14–16 fo...