On a semilinear parabolic equation with time-dependent source term on infinite graphs
Abstract
Abstract We are concerned with semilinear parabolic equations, with a time-dependent source term of the form $$h(t)u^q$$ h ( t ) u q with $$q>1$$ q > 1 , posed on an infinite graph. We assume that the bottom of the $$L^2$$ L 2 -spectrum of the Laplacian on the graph, denoted by $$\lambda _1(G)$$ λ 1 ( G ) , is positive. In dependence of q , h ( t ) and $$\lambda _1(G)$$ λ 1 ( G ) , we show global in time existence or finite time blow-up of solutions.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Numerical methods in inverse problems
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of Evolution Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 26
- Issue
- 1
- Publication date
- 18 January 2026
- Language
- EN