Sep 2026· Studia Universitatis Babeş-Bolyai. Mathematica· Vol 71, pp. 399-420· 0 citations· 47 references
Abstract
In this paper, we consider an initial-boundary value problem for the following mixed pseudo parabolic p-Laplacian type equation with logarithmic nonlinearity on a bounded and regular domain. By adapting the first-order differential inequality method, we establish a blow-up criterion for the solutions and obtain an upper bound for the blow-up time. Besides, we show that blow-up may be prevented under appropriate smallness conditions on the initial datum, in which case we also establish decay estimates in the \(H_0^1(\Omega)\)-norm as \(t\to+\infty\). We also give a two-dimensional numerical example to confirm the validity of our theoretical results.
We study the local asymptotic behavior of nonnegative type I blow-up solutions to semilinear heat equations with nonlinearities that need not be scale invariant. Using a quasi-similarity transformation adapted to the associated ordinary differential equation, we establish locally uniform convergence to a constant profi...
Y. Fujishima, Ryoto Ichiya, Norisuke Ioku· 0 citations
Abstract In this paper, we study a nonlinear fractional boundary value problem involving a p-Laplacian-type ψ-Hilfer operator with a logarithmic source term under homogeneous Dirichlet boundary conditions in a one-dimensional domain Ω ⊂ ℝ {\Omega\subset\mathbb{R}} . The logarithmic nonlinearity introduces slow-growth e...
S. Boulaaras, A. Sabiry· Georgian Mathematical Journa...· 0 citations
We study finite-time blow-up for a semilinear shifted Tricomi equation with decreasing propagation speed and an oscillatory scale-invariant mass. We focus on the Strauss-type critical regime and prove that every weak solution with finite speed of propagation, arising from nonnegative nontrivial energy data satisfying a...
Diego Marcon, Wanderley Nunes Do Nascimento, Matheus C. Santos· 0 citations
We consider the initial value problem of the semilinear heat equation in the Fujita supercritical range for which global-in-time solutions may exist. The main result shows the existence of a separating norm $\|\cdot\|_X$ in the sense that, for nonnegative initial data $u_0\in L^\infty(\mathbf{R}^n)$, the smallness of $...
Our aim in this work is to study the existence of global solutions and blow-up phenomena in finite time of the following quasilinear dissipative Kirchhoff’s string problem:
with initial conditions and where the resistance modules and the external force.
A combination of the Faedo-Galerkin approximation and the Bana...
