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math.AP2024
Radial blow-up standing solutions for the semilinear wave equation
Maissâ Boughrara, Hatem Zaag
We consider the semilinear wave equation with a power nonlinearity in the radial case. Given , we construct a blow-up solution such that the solution near con…
math.AP2024
Standing Sphere Blow-up Solutions to The Nonlinear Heat Equation
Senhao Duan, Nejla Nouaili, Hatem Zaag
In this paper, we construct a singular standing ring solution of the nonlinear heat in the radial case. We give rigorous proof for the existence of a ring blow-up solution in finit…
math.AP2024
A better bound on blow-up rate for the superconformal semilinear wave equation
Mohamed Ali Hamza, Hatem Zaag
We consider the semilinear wave equation in higher dimensions with superconformal power nonlinearity. The purpose of this paper is to give a new upper bound on the blow-up rate in…