Properties of positive solutions for a nonlocal nonlinear diffusion equation with nonlocal nonlinear boundary condition

Robust Stability of Nonlinear Diffusion Fuzzy Neural Networks with Parameter Uncertainties and Time Delays

“…Since then, a lot of research has been done on BAM CGNNs models ( [7,[9][10][11]). Besides, owing to biological engineering backgrounds and population dynamics, economics, physical engineering, and other reasons, the stability of nonlinear diffusion systems have received widespread attention [11][12][13][14][15][16][17]. For example, in [11], the author studied the following nonlinear diffusion fuzzy system, involved to time-delay BAM CohenGrossberg neural networks.…”

Global existence of solutions of initial boundary value problem for nonlocal parabolic equation with nonlocal boundary condition

“…In particular, the blow-up problem for nonlocal parabolic equations with boundary condition (2) was investigated in literature. [25][26][27][28][29][30][31][32] So, for example, Cui et al 25 studied (1)-(3) with b(x, t) ≡ 0, a(x, t) ≡ a(x) and k(x, , t) ≡ k(x, ), and problem (1)-(3) with r = 0, a(x, t) ≡ 1, b(x, t) ≡ b > 0 and k(x, , t) ≡ k(x, ) was considered in Mu et al 30 Gladkov and Guedda 8 studied (1)-(3) with a(x, t) ≡ 0. The existence of classical local solutions and the comparison principle for (1)-(3) were proved in Gladkov and Kavitova.…”

“…Initial-boundary value problems for nonlocal parabolic equations with nonlocal boundary conditions were considered in many papers also (see, for example, [4,7,9,10,26,27,34]). In particular, blow-up problem for nonlocal parabolic equations with boundary condition (1.2) was investigated in [5,8,25,28,29,31,35,36]. So, for example, the authors of [5] studied (1.1)-(1.3) with b(x, t) ≡ 0, a(x, t) ≡ a(x) and k(x, y, t) ≡ k(x, y), and problem (1.1)-(1.3) with r = 0, a(x, t) ≡ 1, b(x, t) ≡ b > 0 and k(x, y, t) ≡ k(x, y) was considered in [31].…”

New Stability Criterion for Takagi‐Sugeno Fuzzy Cohen‐Grossberg Neural Networks with Probabilistic Time‐Varying Delays

“…But the success of these applications largely depends on whether the system has some stability, and so people began to be interested in the stability analysis of the system. In recent decades, reaction-diffusion neural networks have received much attention ( [7][8][9][10][11][12][13]), including various Laplacian diffusion ( [6,[14][15][16][17][18][19][20]). Besides, people are paying more and more attention to fuzzy neural network system ( [21][22][23][24][25][26][27][28][29][30][31][32][33][34]), due to encountering always some inconveniences such as the complicity, the uncertainty, and vagueness ( [27,[35][36][37]).…”