Blow-up time estimates in nonlocal reaction-diffusion systems under various boundary conditions

This paper deals with the question of blow-up of solutions to nonlocal reaction-diffusion systems under various boundary conditions. Specifically, conditions on data are introduced to avoid the blow-up of the solution, and when the blow-up occurs, explicit lower and upper bounds of blow-up time are derived

A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term

In this paper we study a initial-boundary value problem for 4th order hyperbolic equations with weak and strong damping terms and superlinear source term. For blow-up solutions a lower bound of the blow-up time is derived. Then we extend the results to a class of equations where a positive power of gradient term is introduced

Decay in chemotaxis systems with a logistic term

This paper is concerned with a general fully parabolic Keller-Segel system, defined in a convex bounded and smooth domain Ω of RN , for N ∈ {2, 3}, with coefficients depending on the chemical concentration, perturbed by a logistic source and endowed with homogeneous Neumann boundary conditions. For each space dimension, once a suitable energy function in terms of the solution is defined, we impose proper assumptions on the data and an exponential decay of such energies is established

Best Possible Maximum Principles for Fully Nonlinear Elliptic Partial Differential Equations

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Exponential decay bounds for nonlinear heat problems with Robin boundary conditions

We investigate the behavior of the solution of a nonlinear heat problem, when Robin conditions are prescribed on the boundary ∂Ω×(t > 0), Ω a bounded R2 domain. We determine conditions on the geometry and data sufficient to preclude the blow up of the solution and to obtain an exponential decay bound for the solution and its gradient