We study the Cauchy problem for the semilinear structural damped wave equation with
source term with σ∈(0, 1] in space dimension n≥ 2 and with a positive constant μ. We are …

In this paper, we study diffusion phenomena for the wave equation with structural damping
utt− Δ u+ 2 a (− Δ) σ ut= 0, u (0, x)= u 0 (x), ut (0, x)= u 1 (x), with a> 0 and σ∈(0, 1/2). We …

In this article, we analyze a spatio-temporally nonlocal nonlinear parabolic equation. First,
we validate the equation by an existence-uniqueness result. Then, we show that blowing-up …

In this paper we study the global existence of small data solutions to utt−△ u+ 2 a (−△) σ
ut=| u| p, u (0, x)= u 0 (x), ut (0, x)= u 1 (x), where a> 0, σ∈(0, 1/2] and p> 1. Assuming small …

GLOBAL SOLUTIONS FOR A NONLINEAR INTEGRAL EQUATION WITH A GENERALIZED
HEAT KERNEL Kazuhiro Ishige Tatsuki Kawakami Kanako Kobaya Page 1 DISCRETE AND …

This paper is concerned with a nonlinear integral equation $$(P)\qquad u (x, t)=\int_ {{\bf R}^
N} G (xy, t)\varphi (y) dy+\int_0^ t\int_ {{\bf R}^ N} G (xy, ts) f (y, s: u) dyds,\quad $$ where …

We consider the Cauchy problem in R n, n≥ 1, for a semilinear damped wave equation with
nonlinear memory. Global existence and asymptotic behavior as t→∞ of small data …

In this paper, we discuss a test function method to obtain nonexistence of global-in-time
solutions for higher order evolution equations with fractional derivatives and a power …

Main purpose of this paper is to study the following semi-linear structurally damped wave
equation with nonlinearity of derivative type: $$ u_ {tt}-\Delta u+\mu (-\Delta)^{\sigma/2} u_t …

In this paper we obtain the precise description of the asymptotic behavior of the solution u of
the fractional diffusion equation \partial_tu+(-Δ)^θ2u=0\quadin\bfR^N*(0,∞) with the initial …