Nonnegative solutions for a class of singular parabolic problems involving p-Laplacian

On the existence of weak solutions for a class of singular reaction diffusion systems

“…Proof. The uniform estimate (4.1) for the sequence {u n } follows directly by Proposition 2.13 in [11] with some abbreviations that go along with our problem. For simplicity we suppose v 0,n (x) = 0.…”

“…The difficulties in this work are similar to those in [9][10][11][12][13][14], and the techniques are of the same spirit, but specific new difficulties due to the nature of the system must be handled.…”

“…In this work, we are interested in the study of a singular reaction diffusion system. For modeling and mathematical analysis of this type of problem, several methods have been proposed; see for example, [1,2], [4], [5], [7], [9][10][11][12][13][14], [21][22][23][24], [29][30][31][32][33], [37] and corresponding references therein.…”

“…Before stating the main result of this work, it is worth mentioning that several mathematicians have dealt with this type of problem using various analytical and numerical techniques and methods, under different hypotheses as appropriate, see for example, [4], [7], [9][10][11][12][13][14] and [37].…”

On nonlinear parabolic equations with singular lower order term

“…In the same concept the authors in [23] proved the existence of solution to problem with 𝛾 > 0, f is a nonnegative function on , and is a nonnegative bounded Radon measures on . Hence Charkaoui and Alaa [7] established the existence of weak periodic solution to singular parabolic problems with 𝛾 > 0 and f is a nonnegative integrable function periodic in time with period T. Let us observe that we refer to [8,9,11,17,24] for more details on singular parabolic problems.…”