Large Time Behavior of Solutions of a Semilinear Parabolic Equation with a Nonlinear Dynamical Boundary Condition

Nonsymmetric solutions of a nonlinear boundary value problem

“…In the recent paper [14], (1.1) was studied for p, q ∈ R, and its solvability was examined for p −1, 0 q (p + 1)/2 and p > −1, q > (p + 1)/2, but only symmetric solutions were dealt with in the latter case. Further extensions of the results from [5] can be found in [1], [3], [4], [7], [8], [9]. It was shown in [5], Theorems 3.1 and 3.2, that assuming p, q > 1, (1.1) possesses positive nonsymmetric solutions only for q > (p + 1)/2.…”

A Mathematical Study of a Bistable Nematic Liquid Crystal Device

“…1,3,[10][11][12]18 The main scheme of proving global existence for parabolic problems with nonlinear boundary conditions follows; 1 see also Ref. 17 for an accessible introduction to Amann's theory.…”

“…In Ref. 12, also based on the same functional approach, further results on the large time behavior of solutions are obtained for a specific type of semilinear problem. Since in our case we impose a Dirichlet type boundary condition on a part of the boundary, which is not considered in Refs.…”

Blow-up and continuation of solutions for some semilinear parabolic

“…The study of the finite time blow-up and the global existence of solutions for this problem was started in [7] and independently in [19], and later the results were improved by many authors ( see [1], [3], [4], [8], [9], [21] [22], [23]), and also extended to quasilinear parabolic equations ( see [1], [10], [11], [15], [17], [24]). It is known that the dynamics of (1.1) is classified into three cases:…”