Superlinear Parabolic Problems

By Pavol Quittner, Philippe Souplet. Birkhäuser Advanced Texts Basler Lehrbücher, 2007

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Existence and nonexistence of solutions for the heat equation with a superlinear source term (2016, background): “We also refer to [14] and [19], which include good references concerning parabolic equations.”
A global branch approach to normalized solutions for the Schrödinger equation (2021, neutral): “Then from (2.1) and using the fact that u belongs to At this point, under our assumption on γ > 2 , the conclusion follows by [31, Theorem 8.4].”
Global existence for reaction–diffusion systems with dissipation of mass and quadratic growth (2018, neutral): “…that global existence is no longer trivial when the d i are not equal (a case which is indeed relevant in chemical reactions) and there is an abundant mathematical literature on this question (see, e.g., [18, Section 33] and [15] for surveys, and see also further references in Remark 1 below).”
Dissipative Gradient Nonlinearities Prevent δ$\delta$ ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models (2024, neutral): “The study of gradient terms in parabolic equations, and their impact on the possibility of blow-up, in the sense that u tends to a coalescence and ceases existing at some finite time (we will be more clear below), is a classical topic; we mention [5, 24, 11] and [39, Sect.”