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Displaying 141 –
160 of
445
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic
PDEs are examined. The schemes under consideration are discontinuous in time but
conforming in space and of arbitrary order. Stability estimates are presented in the
natural energy norms and at arbitrary times, under minimal regularity assumptions.
Space-time error estimates of arbitrary order are derived, provided that the natural
parabolic regularity is present....
The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the and error estimates are established. At the end...
The G-function formalism has been
widely used in the context of evolutionary games for identifying
evolutionarily stable strategies (ESS). This formalism was
developed for and applied to point processes. Here, we
examine the G-function
formalism in the settings of spatial evolutionary
games and strategy dynamics, based on reaction-diffusion models. We start
by
extending the point process maximum principle to reaction-diffusion models
with homogeneous, locally stable surfaces.
We then develop...
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
The results of this paper concern exact controllability to the
trajectories for a coupled system of semilinear heat equations. We
have transmission conditions on the interface and Dirichlet boundary
conditions at the external part of the boundary so that the system can be
viewed as a single equation with discontinuous coefficients in the
principal part. Exact controllability to the trajectories is proved when we
consider distributed controls supported in the part of the domain where the
diffusion...
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
We consider a class of degenerate reaction-diffusion equations on a bounded domain with nonlinear flux on the boundary. These problems arise in the mathematical modelling of flow through porous media. We prove, under appropriate hypothesis, the existence and uniqueness of the nonnegative weak periodic solution. To establish our result, we use the Schauder fixed point theorem and some regularizing arguments.
This paper is devoted to the existence and uniqueness of solutions for gradient systems of evolution which involve gradients taken with respect to time-variable inner products. The Gelfand triple considered in the setting of this paper is such that the embedding is only continuous.
We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.
Currently displaying 141 –
160 of
445