Abstract

This work presents optimal conditions for the existence of global solutions for the coupled parabolic system: ut-Delta u = h(t)f(v) and vt-Delta v = l(t)g(u) in ohm x (0, T ) with the Dirichlet boundary conditions. Here, ohm subset of RN is a bounded or unbounded domain, the initial data belong to [C0(ohm)]2, and the functions f, g, h, l is an element of C[0, infinity). We also study the coupled parabolic system with degenerate coefficients: ut-div(omega(x)del u) = h(t)f(v) and vt-div(omega(x)del v) = l(t)g(u) in RN x (0, T ), where omega belong to the class A2 of Muckenhoupt functions and may exhibit singularities along the line x1 = 0. This problem is related to the fractional Laplacian through the Caffarelli-Silvestre extension given in [2]. In addition, critical Fujita-type exponents are derived for both systems. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.