This research reveals necessary conditions for blow-up solutions in nonlinear reaction-diffusion equations, indicating gaps in prior understanding.
This paper investigates the global and nonglobal existence of solutions to nonlinear reaction‐diffusion equations with a general nonlinearity and time‐dependent sources defined on cones of Euclidean spaces. More precisely, the purpose of this work is to give a necessary and sufficient condition for the equations to have only blow‐up solutions. As a matter of fact, this problem has been left open for about 30 years, since the work by P. Meier.
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Chung et al. (2025) studied this question.
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