"The goal of this paper is to study the nonexistence nontrivial solutions following Cauchy problem $$\left\{ \begin{array}{ll} u_{tt}+(-\Delta)^{\beta/2} u+u_{t}=\displaystyle\int_{0}^{t}\left(t-\tau \right) ^{-\gamma}\left\vert u(\tau ,\cdot) \right\vert^{p}d\tau,\\ \cr u(0,x)=u_{0}(x),\quad u_t(0,x)=u_1(x),\quad x\in\mathbb{R}^n, \end{array}\right.$$ where $p>1,\ 0<\gamma <1,\,\, \be...

In Part I of this series [A. Poveda, A. Rinot and D. Sinapova, Sigma-Prikry forcing I: The axioms, Canad. J. Math. 73(5) (2021) 1205–1238], we introduced a class notions which call [Formula: see text]-Prikry, showed that many the known Prikry-type center around singular cardinals countable cofinality are text]-Prikry. We given text]-Prikry poset text] text]-name for non-reflecting stationary se...

* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...

We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for ut = u∆u + u ∫ Ω |∇u| in bounded domains Ω ⊂ R which arises in game theory. We prove that solutions converge to 0 if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with ...

We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow up of solutions subject to sufficiently large initial data provided that the reaction term ”overpowers” the nonlinear diffusion in a certain sense. Secondly, under related assumptions o...

We study in detail the blow-up procedure described in [BTW01]. We obtain a structure theorem for coreless polygroups as a double quotient space G/H, and a polygroup chunk theorem. Seeking to remove the arbitrary parameter needed for the blow-up, we find canonical ∅-invariant groupoids G > H analogous to G and H above, and show that H contains precisely all the arbitrary choices related to the b...

Stability of blow-up proole for equation of the type u t = u + juj p?1 u Abstract In this paper, we consider the following nonlinear equation u t = u + juj p?1 u u(:; 0) = u 0 ; (and various extensions of this equation, where the maximum principle do not apply). We rst describe precisely the behavior of a blow-up solution near blow-up time and point. We then show a stability result on this beha...