相关论文: Gradient estimates for solutions of the Lam\'e sys…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…

A simple criterion of the existence of (type-I) blow-up solutions for nonautonomous ODEs is provided. In a previous study [Matsue, SIADS, 24(2025), 415-456], geometric criteria for characterizing blow-up solutions for nonautonomous ODEs are…

An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.

We study conjectures on the dimension of linear systems on the blow-up of P^2 and P^3 at points in very general position. We provide algorithms and Maple codes based on these conjectures.

In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations. Under suitable assumptions, lower and upper bounds of explosion times are obtained by using explicit…

In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, the stability of…

We consider the blowup rate for blowup solutions to $L^2$-critical, focusing NLS with a harmonic potential and a rotation term. Under a suitable spectral condition we prove that there holds the "$\log$-$\log$ law" when the initial data is…

For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large class of these equations, we show that some of the solutions which do not blow up actually tend to…

We derive reduced finite dimensional ODE models starting from one dimensional lubrication equations describing coarsening dynamics of droplets in nanometric polymer film interacting on a hydrophobically coated solid substrate in the…

We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form $$ \left\{ \begin{aligned} \Delta_{p} u&=v^{m}|\nabla u|^{\alpha}&&\quad\mbox{ in }\Omega,\\ \Delta_{p} v&=v^{\beta}|\nabla u|^{q}…

We consider equivariant wave maps from $\mathbb{R}^{d+1}$ to $\mathbb{S}^d$ in supercritical dimensions $3\leq d\leq 6$. Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable…

We obtain uniform in time $L^\infty$-bounds for the solutions to a class of thermo-diffusive systems. The nonlinearity is assumed to be at most sub-exponentially growing at infinity and have a linear behavior near zero.

We study systems of nonlinear ordinary differential equations where the dominant term, with respect to large spatial variables, causes blow-ups and is positively homogeneous of a degree $1+\alpha$ for some $\alpha>0$. We prove that the…

In this paper, we consider the semi-linear wave systems with power-nonlinearities and a large class of space-dependent damping and potential. We obtain the same blow-up regions and the lifespan estimates for three types wave systems,…

In this paper, we consider the semi-linear wave systems with power-nonlinearities and space-dependent dampings and potentials. We obtain the blow-up regions for three types wave systems as well as the lifespan estimates.

We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on preceding studies, a variant of closed embeddings of phase spaces…

We consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true…

We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which…

We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are…