1,720,993 research outputs found
Some properties of solutions to nonlinear parabolic problems with Neumann conditions
No full textWe investigate the behavior of the solution of a nonlinear parabolic
problem, when Neumann conditions are prescribed on the boundary a bounded R^N domain. We determine conditions on the geometry and data
to insure a decay bound for the solution and its gradient
Remarks on blow up time for solutions of a nonlinear diffusion systems with time dependent coefficients
Full text linkWe investigate the blow-up of the solutions to a nonlinear parabolic system with Robin boundary conditions and time dependent coefficients. We derive sufficient conditions on the nonlinearities and the initial data in order to obtain explicit lower and upper bounds for the blow up time t
Bounds for blow-up time in nonlinear parabolic systems under various boundary conditions
No full textwe consider blow-up solutions to parabolic systems, coupled through their nonlinearities under various boundary conditions with nonlinearities depending on the gradient solution. To obtain a lower bound to blow up time t* for the vector solution, Sobolev-type inequalities are introduced to make use of a differential inequality technique. In addition for Dirichlet systems sufficient conditions are introduced to derive an upper bound for t* and to have a criterion for the global existence of the vector solution
Explicit decay estimates for solutions to nonlinear parabolic systems
No full textThe aim of this paper is to investigate a class of nonlinear parabolic systems with initial and boundary values of Dirichlet type, when the nonlinearities depend on the gradient of the solution. Sufficient conditions on data are established in order to preclude blow up and to deduce that the solution decays exponentially in time. Moreover, an upper of its gradient is derived
Optimization in problems involving the p-Laplacian
No full textWe minimize the energy integral , where is a bounded positive function that varies in a class of rearrangements, , and is a solution of Also we maximize the first eigenvalue , where For both problems, we prove existence, uniqueness, and representation of the optimizers
Maximum principles and decay estimates for parabolic systems under Robin Boundary conditions
No full textOn global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients
No full textThis paper deals with the blow-up of the solutions to a class of nonlinear parabolic equations with Dirichlet boundary condition and time dependent coefficients. Under some conditions on the data and geometry of the spatial domain, explicit upper and lower bounds for the blow-up time are derived. Moreover, the influence of the data on the behaviour of the solution is investigated to obtain global existence
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
Continuous dependence results for parabolic problems under Robin boundary conditions
No full textWe investigatew contnuous dependence on initial data for solutions of a nonlinear parabolic problem, when Robin conditions are prescribed on the boundary a bounded R^2 domai
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