All Outputs (3)

Non-existence of local solutions for semilinear heat equations of Osgood type (2013)
Journal Article
Laister, R., Robinson, J. C., & Sierżęga, M. (2013). Non-existence of local solutions for semilinear heat equations of Osgood type. Journal of Differential Equations, 255(10), 3020-3028. https://doi.org/10.1016/j.jde.2013.07.007

We establish non-existence results for the Cauchy problem of some semilinear heat equations with non-negative initial data and locally Lipschitz, non-negative source term f. Global (in time) solutions of the scalar ODE v;=f(v) exist for v(0)>0 if and... Read More about Non-existence of local solutions for semilinear heat equations of Osgood type.

Gaussian lower bounds on the Dirichlet heat kernel and non-existence of local solutions for semilinear heat equations of Osgood type (2013)
Journal Article
Laister, R., Robinson, J. C., & Sierzega, M. (2013). Gaussian lower bounds on the Dirichlet heat kernel and non-existence of local solutions for semilinear heat equations of Osgood type

We give a simple proof of a lower bound for the Dirichlet heat kernel in terms of the Gaussian heat kernel. Using this we establish a non-existence result for semilinear heat equations with zero Dirichlet boundary conditions and initial data in $L^q... Read More about Gaussian lower bounds on the Dirichlet heat kernel and non-existence of local solutions for semilinear heat equations of Osgood type.

Convergence to equilibrium in degenerate parabolic equations with delay (2013)
Journal Article
Laister, R., & Laister, R. (2013). Convergence to equilibrium in degenerate parabolic equations with delay. Nonlinear Analysis: Theory, Methods and Applications, 81, 200-210. https://doi.org/10.1016/j.na.2012.10.019

© 2012 Elsevier Ltd In [11], Busenberg & Huang (1996) showed that small positive equilibria can undergo supercritical Hopf bifurcation in a delay-logistic reaction–diffusion equation with Dirichlet boundary conditions. Consequently, stable spatially... Read More about Convergence to equilibrium in degenerate parabolic equations with delay.