相关论文: Blow-up of solutions to a p-Laplace equation

The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. Much attention has been devoted to the blow-up estimate, especially in two dimensions, for the…

In the perfect conductivity problem of composite material, the electric field concentrates in a narrow region in between two inclusions and always becomes arbitrarily large when the distance between inclusions tends to zero. To characterize…

In the perfect conductivity problem, it is interesting to study whether the electric field can become arbitrarily large or not, in a narrow region between two adjacent perfectly conducting inclusions. In this paper, we show that the…

When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbitrary large. We establish both the pointwise upper bound and…

This paper deals with the blow-up properties of positive solutions to a system of two heat equations.

In composite materials, the inclusions are frequently spaced very closely. The electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusions will always become arbitrarily large. In this paper, we…

We investigate the $p-$Laplace heat equation $u_t-\Delta_p u=\zeta(t)f(u)$ on a bounded smooth domain $\Omega\subset\mathbb{R}^N$. Using differential inequalities arguments, we prove blow-up results under suitable conditions on $\zeta, f$,…

We generalize results of P.M.H. Wilson describing situations where the blow up of the conductor ideal of a scheme coincides with the normalization.

In the present note, we address the question about behavior of $L_3$-norm of the velocity field as time $t$ approaches blow-up time $T$. It is known that the upper limit of the above norm must be equal to infinity. We show that, for…

A theoretical study of small thermal and electromagnetic perturbations in type-II superconductors is studied in the flux creep regime with a power-law voltage-current characteristics. The space-time evolution of temperature and electric…

We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in $H^{1}_{loc}\times L^2_{loc}$ or some times in $ W^{1,\infty}\times…

We find a smooth solution of the 2D Euler equation on a bounded domain which exists and is unique in a natural class locally in time, but blows up in finite time in the sense of its vorticity losing continuity. The domain's boundary is…

Let $\Omega$ be a bounded smooth domain in $\RR^N$. We consider the problem $u_t= \Delta u + V(x) u^p$ in $\Omega \times [0,T)$, with Dirichlet boundary conditions $u=0$ on $\partial \Omega \times [0,T)$ and initial datum $u(x,0)= M \phi…

We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…

We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region…

The blowup is studied for the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative…

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by…

We prove a blow-up criterion for the solutions to the $\nu$-dimensional Patlak-Keller-Segel equation in the whole space. The condition is new in dimension three and higher. In dimension two it is exactly Dolbeault's and Perthame's blow-up…

For a singular Liouville equation, it is plausible that a non-simple blowup phenomenon occurs around a quantized singular pole. The presence of complex blowup profiles of bubbling solutions presents substantial challenges in applications.…

We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f(u)$. We always assume that the infimum of the spectrum of the…