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Supersolutions and stabilization of the solutions of the equation∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u), Part II.

Abderrahmane El Hachimi, François De Thélin (1991)

Publicacions Matemàtiques

In this paper we consider a nonlinear parabolic equation of the following type:(P)      ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u)with Dirichlet boundary conditions and initial data in the case when 1 < p < 2.We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with (P).

Supersymmetry and Ghosts in Quantum Mechanics

Robert, Didier (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 81Q60, 35Q40.A standard supersymmetric quantum system is defined by a Hamiltonian [^H] = ½([^Q]*[^Q] +[^Q][^Q]*), where the super-charge [^Q] satisfies [^Q]2 = 0, [^Q] commutes with [^H]. So we have [^H] ≥ 0 and the quantum spectrum of [^H] is non negative. On the other hand Pais-Ulhenbeck proposed in 1950 a model in quantum-field theory where the d'Alembert operator [¯] = [(∂2)/( ∂t2)] − Δx is replaced by fourth order operator [¯]([¯] + m2), in order to...

Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in 𝐙 d

Wei-Min Wang (1999)

Journées équations aux dérivées partielles

By using a supersymmetric gaussian representation, we transform the averaged Green's function for random walks in random potentials into a 2-point correlation function of a corresponding lattice field theory. We study the resulting lattice field theory using the Witten laplacian formulation. We obtain the asymptotics for the directional Lyapunov exponents.

Supplementary balance laws for Cattaneo heat propagation

Serge Preston (2013)

Communications in Mathematics

In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (shortly SBL) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature ( λ 0 ( ϑ ) , K A ( ϑ ) , A = 1 , 2 , 3 ). The requirements of the II law of thermodynamics...

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