Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy

Global Existence and Asymptotic Behavior of Weak Solutions to Nonlinear Thermoviscoelastic Systems with Clamped Boundary Conditions

This paper is concerned with global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to nonlinear thermoviscoelastic systems with clamped boundary conditions. The constitutive assumptions for the Helmholtz free energy include the model for the study of phase transitions in shape memory alloys. To describe phase transitions between different configurat...

Asymptotic Behavior of Coupled Dynamical Systems with Multiscale Aspects

We study the asymptotic behaviour, as time variable t goes to +∞, of nonautonomous dynamical systems involving multiscale features. As a benchmark case, given H a general Hilbert space, Φ : H → R ∪ {+∞} and Ψ : H → R ∪ {+∞} two closed convex functions, and β a function of t which tends to +∞ as t goes to +∞, we consider the differential inclusion ẋ(t) + ∂Φ(x(t)) + β(t)∂Ψ(x(t)) ∋ 0. This system ...

Asymptotic L1-decay of Solutions of the Porous Medium Equation to Self-similarity

We consider the flow of gas in an N-dimensional porous medium with initial density v0(x) ≥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = ∆vm where m > 1 is a physical constant. Assuming that ∫ (1 + |x|2)v0(x)dx < ∞, we prove that v(x, t) behaves asymptotically, as t → ∞, like the Barenblatt-Pattle solution V(|x|, t). We prove that the L1-distance decays ...

Asymptotic Behavior of Energy Solutions to a Two Dimensional Semilinear Problem with Mixed Boundary Condition

Pergamon Asymptotic Behavior of Energy Solutions to a Two-dimensional Semilinear Problem with Mixed Boundary Condition

where: • f~ is a C °'1 and bounded domain in Rz; • 0f~ consists of two pieces F0 and F1, where the one-dimensional Hausdorff measure of F o is greater than 0; • F0 is smooth and F1 is piecewise smooth; • F0 and 1"1 are relatively closed in 0f~; • v is the unit outer normal of f~; • p is a large parameter. In this work, we shall only consider the least energy solutions, although the method can b...