1,720,999 research outputs found
Applications of Best Possible maximum Principles to parabolic problems in non-convex domains
No full textQualitative properties for solutions of reaction-diffusion parabolic systems and their gradients
No full textThe aim of this paper is to investigate a class of reaction–diffusion parabolic systems with initial and boundary values of 4
Dirichlet type. Sufficient conditions on data are established in order to preclude blow-up and obtain that the solutions and their 5
gradients decay exponentially in time
Explicit estimates for blow-up solutions to parabolic systems under nonlocal boundary conditions
No full textThis paper deals with a nonlinear parabolic system, which contains a nonlocal
term in the boundary conditions. Explicit estimates from above and from
below for the blow-up time are obtained by means of suitable inequalities and
appropriate auxiliary functions
Upper and lower solutions in quasilinear parabolic boundary value problems
No full textThe authors study a class of initial boundary value problems associated with parabolic quasilinear equations: by introducing special auxiliary functions, upper and lower solutions are obtained, which turn out to be sharp in the sense that they coincide with the solution in particular situations
Decay estimates for solutions of a class of parabolic problems arising in filtration through porous media
No full textExponential decay bounds for nonlinear heat problems with Robin boundary conditions
No full textWe 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
Sharp upper and lower solutions in some parabolic problems
No full textIn this paper we construct upper and lower solutions for a class of parabolic initial-boundary value problems in terms of the solution of the St-Venant problem and first eigenvalue problem. These bounds are sharp in the sense that they coincide with the exact solution in particular situations
Bounds for blow-up time in nonlinear parabolic system
No full textWe consider a nonlinear parabolic system with Neumann boundary conditions which solution may blow up in finite time t*: We determine a lower bound for t* by using a Sobolev type inequality. In addition an upper bound for t* is obtained, under alternative conditions on the non linearities
Blow-up phenomena in reaction-diffusion systems
No full textIn this paper we deal with the blow-up phenomena of solutions to two different classes of reaction-diffusion systems coupled through nonlinearities with nonlinear boundary conditions. By using a differential inequality technique, we derive upper and lower bounds for the blow-up time, if blow-up occurs. Moreover by introducing suitable auxiliary functions, we give suffcient conditions on data in order to obtain global existence
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