A complete characterization of Fujita's blow-up solutions for discrete p-Laplacian parabolic equations under the mixed boundary conditions on networks

2021 ◽  
Vol 497 (1) ◽  
pp. 124859
Author(s):  
Soon-Yeong Chung ◽  
Jaeho Hwang
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Blow Up ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Complete Characterization

Heterogeneous Elliptic BVPs with a Bifurcation-Continuation Parameter in the Nonlinear Mixed Boundary Conditions

2020 ◽  
Vol 20 (1) ◽  
pp. 31-51
Author(s):  
Santiago Cano-Casanova
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Blow Up ◽  
Mixed Boundary ◽  
Elliptic Boundary ◽  
Global Bifurcation ◽  
Mixed Boundary Conditions ◽  
Elliptic Boundary Value ◽  
New Findings ◽  
Continuation Parameter

AbstractThis article ascertains the global structure of the diagram of positive solutions of a very general class of elliptic boundary value problems with spatial heterogeneities and nonlinear mixed boundary conditions, considering as bifurcation-continuation parameter a certain parameter γ that appears in the boundary conditions. In particular, in this work are obtained, in terms of such a parameter γ, the exact decay rate to zero and blow-up rate to infinity of the continuum of positive solutions of the problem, at the bifurcations from the trivial branch and from infinity. The new findings of this work complement, in some sense, those previously obtained for Robin linear boundary conditions by J. García-Melián, J. D. Rossi and J. C. Sabina de Lis in 2007. The main technical tools used to develop the mathematical analysis carried out in this paper are local and global bifurcation, continuation, comparison and monotonicity techniques and blow-up arguments.

scholarly journals Systems with Local and Nonlocal Diffusions, Mixed Boundary Conditions, and Reaction Terms

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Mauricio Bogoya ◽  
Julio D. Rossi
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Blow Up ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Asymptotic Bounds ◽  
Blowing Up ◽  
Blow Up Rate ◽  
Blowing Up Solutions

We study systems with different diffusions (local and nonlocal), mixed boundary conditions, and reaction terms. We prove existence and uniqueness of the solutions and then analyze global existence vs blow up in finite time. For blowing up solutions, we find asymptotic bounds for the blow-up rate.

Stabilizability of Infinite-Dimensional Systems by Finite-Dimensional Controls

2019 ◽  
Vol 19 (4) ◽  
pp. 797-811 ◽  
Author(s):  
Jean-Pierre Raymond
Keyword(s):  
Boundary Conditions ◽  
Control Systems ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Oseen Equations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional

AbstractIn this paper, we consider control systems for which the underlying semigroup is analytic, and the resolvent of its generator is compact. In that case we give a characterization of the stabilizability of such control systems. When the stabilizability condition is satisfied the system is also stabilizable by finite-dimensional controls. We end the paper by giving an application of this result to the stabilizability of the Oseen equations with mixed boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document