Related papers: The lifespan of solutions to wave equations with w…
We study the initial value problem for a defocusing semi-linear wave equation with spatially growing nonlinearity. By employing Moser-Trudinger type inequalities and Strichartz estimates, we establish global well-posedness in the energy…
In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…
Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is…
We study the Cauchy problem for a semilinear heat equation with initial data non-rarefied at $\infty$. Our interest lies in the discussion of the effect of the non-rarefied factors on the life span of solutions, and some sharp estimates on…
By assuming certain local energy estimates on $(1+3)$-dimensional asymptotically flat space-time, we study the existence portion of the \emph{Strauss} type wave system. Firstly we give a kind of space-time estimates which are related to the…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
The problem of blow up of solutions to the initial boundary value problem for non-autonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions of blow up in a…
This work is directed towards investigating the fate of three-dimensional long perturbation waves in a plane incompressible wake. The analysis is posed as an initial-value problem in space. More specifically, input is made at an initial…
We consider the hyperboloidal initial value problem for the cubic focusing wave equation. Without symmetry assumptions, we prove the existence of a co-dimension 4 Lipschitz manifold of initial data that lead to global solutions in forward…
We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and…
We consider the equations of a multi-velocity model of a binary mixture of viscous compressible fluids (two-fluid medium) in the case of one-dimensional barotropic motions. We prove the global (in time) existence and uniqueness of a strong…
In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be…
We give a proof for the existence of a weak solution on the initial-value problem of a non-linear damped propagation
We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms.…
In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we…
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
We investigate the lifespan of solutions to the higher-order semilinear parabolic equation $$u_t+(-\Delta)^m u=|u|^p, \quad x \in \mathbb{R}^n, t>0 $$ with initial data. We focus on the precise asymptotic behavior of the lifespan of…
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of…
In this paper, we study the characteristic initial value problem for a class of nonlinear wave equations with data on a conic light cone in the Minkowski space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class of…