6 papers
Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data
Kotaro Hisa, Jin Takahashi, Erbol Zhanpeisov
We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions t…
Blow-up rate for the subcritical semilinear heat equation in non-convex domains
Hideyuki Miura, Jin Takahashi, Erbol Zhanpeisov
We consider the semilinear heat equation in possibly non-convex and unbounded domains. Our main result shows the nonexistence of type II blow-up for possibly s…
Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy
Qing Liu, Erbol Zhanpeisov
We study a class of fully nonlinear boundary-degenerate elliptic equations, for which we prove that u \equiv 0 is the only solution. Although no boundary conditions are posed toget…
Existence of solutions for time fractional semilinear parabolic equations in Besov--Morrey spaces
Yusuke Oka, Erbol Zhanpeisov
We consider the Cauchy problem for a time fractional semilinear heat equation with initial data belonging to inhomogeneous/homogeneous Besov--Morrey spaces. We present sufficient c…
Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces
Erbol Zhanpeisov
In this paper, we establish the existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces for a large class of initial data including distributions…
Blow-up rate of sign-changing solutions to nonlinear parabolic systems
Erbol Zhanpeisov
We present a blow-up rate estimate for a solution to the parabolic Gross-Pitaevskii and related systems on entire space with Sobolev subcritical nonlinearity. We extend the results…