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Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

Olaf Klein (2004)

Applications of Mathematics

The asymptotic behaviour for t → ∞ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...

Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue

Dimitri Mugnai (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant’s Nodal theorem.

Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue

Dimitri Mugnai (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal theorem.

Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach

Fabio Paronetto (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations ∂ t ( r h u ) - div ( a h · D u ) with r h ( x , t ) ≥ 0 , r h ∈ L ∞ ( Ω × ( 0 , T ) ) . The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain G-convergence for elliptic operators ( r h ≡ 0 ) , G-convergence for parabolic operators ( r h ≡ 1 ) , singular perturbations of an elliptic operator ( a h ≡ a and r h → r , possibly r ≡ 0 ) .

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Currently displaying 161 – 180 of 238