Related papers: Lifespan estimate for the semilinear regular Euler…
In this paper, we consider the blow-up problem of semilinear generalized Tricomi equation. Two blow-up results with lifespan upper bound are obtained under subcritical and critical Strauss type exponent. In the subcritical case, the proof…
We study in this paper the small data Cauchy problem for the semilinear generalized Tricomi equations with a nonlinear term of derivative type $u_{tt}-t^{2m}\Delta u=|u_t|^p$ for $m\ge0$. Blow-up result and lifespan estimate from above are…
In this paper, we prove a blow-up result for a generalized semilinear Euler-Poisson-Darboux equation with polynomially growing speed of propagation, when the power of the semilinear term is a shift of the Strauss' exponent for the classical…
The blow up problem of the semilinear scale-invariant damping wave equation with critical Strauss type exponent is investigated. The life span is shown to be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for…
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical time-dependent damping term (DW). The result is the sharp upper bound of lifespan of solution with respect to the small…
In our recent precious work, we established the finite time blow up result and upper bound of lifespan estimate to the singular Cauchy problem of semilinear Euler-Poisson-Darboux equation in R^n with subcritical power type nonlinearity. By…
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.…
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$V$). The main result of the present paper is to give a solution of the problem and to…
Firstly, we study the equation $\square u = |u|^{q_c}+ |\partial u|^p$ with small data, where $q_c$ is the critical power of Strauss conjecture and $p\geq q_c.$ We obtain the optimal lifespan…
In this paper, we study the finite-time blow up of solutions to the following semilinear wave equation with time-dependent damping \[ \partial_t^2u-\Delta u+\frac{\mu}{1+t}\partial_tu=|u|^p \] in $\mathbb{R}_{+}\times\mathbb{R}^n$. More…
Lifespan estimates for semilinear damped wave equations of the form $\partial_t^2u-\Delta u+\partial_tu=|u|^p$ in a two dimensional exterior domain endowed with the Dirichlet boundary condition are dealt with. For the critical case of the…
In this work, we investigate the influence of general damping and potential terms on the blow-up and lifespan estimates for energy solutions to power-type semilinear wave equations. The space-dependent damping and potential functions are…
In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blow-up study of nonlinear wave…
In this article, we investigate the blow-up for local solutions to a semilinear wave equation in the generalized Einstein - de Sitter spacetime with nonlinearity of derivative type. More precisely, we consider a semilinear damped wave…
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 consider the following semilinear wave equation with time-dependent damping. \begin{align} \tag{NLDW} \left\{ \begin{array}{ll} \partial_t^2 u - \Delta u + b(t)\partial_t u = |u|^{p}, & (t,x) \in [0,T) \times \mathbb{R}^n, \\…
In this note, we derive a blow-up result for a semilinear generalized Tricomi equation with damping and mass terms having time-dependent coefficients. We consider these coefficients with critical decay rates. Due to this threshold nature of…
In this paper, we prove some blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime by using an iteration argument and we derive upper bound estimates for the lifespan. In particular, we will focus on…
This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown…
In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper…