Journal of Evolution Equations Volume 7 Issue 4

Journal Article

Ornstein–Uhlenbeck operators with time periodic coefficients

Prato, Giuseppe; Lunardi, Alessandra

2007 Journal of Evolution Equations

We study the realization of the differential operator $$u \mapsto u_t - L(t)u$$ in the space of continuous time periodic functions, and in L 2 with respect to its (unique) invariant measure. Here L ( t ) is an Ornstein-Uhlenbeck operator in $${\mathbb{R}}^n$$ , such that L ( t + T ) = L ( t ) for...

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Journal Article

Large time behavior of solutions to Newtonian filtration equation with nonlinear boundary sources

Wang, Zejia; Yin, Jingxue; Wang, Chunpeng; Gao, Hang

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0324-9

This paper deals with the exterior problem of the Newtonian filtration equation with nonlinear boundary sources. The large time behavior of solutions including the critical Fujita exponent are determined or estimated. An interesting phenomenon is illustrated that there exists a threshold value...

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Journal Article

Exponential attractors for a class of reaction-diffusion problems with time delays

Grasselli, Maurizio; Pražák, Dalibor

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0326-7

We consider a reaction-diffusion system subject to homogeneous Neumann boundary conditions on a given bounded domain. The reaction term depends on the population densities as well as on their past histories in a very general way. This class of systems is widely used in population dynamics...

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Journal Article

Well-posedness for the system of the Hamilton–Jacobi and the continuity equations

Strömberg, Thomas

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0327-6

Let H (t, x, p ) be a Hamiltonian function that is convex in p . Let the associated Lagrangian satisfy the nonstandard minorization condition $$L(t, x, v) \geq \frac{1}{2} m({\mid v \mid}^2 - \omega^{2}{\mid x \mid}^{2})-C$$ where m > 0, ω > 0, and C ≥ 0 are constants. Under some additional...

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Journal Article

Second order evolution equations with time-dependent subdifferentials

Kubo, Masahiro

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0332-9

We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions on the convex functions and other data, we...

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Journal Article

Kernel estimates for a class of Schrödinger semigroups

Metafune, G.; Spina, C.

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0338-3

We prove short time estimates for the heat kernels of certain Schrödinger operators with unbounded potentials in $${\mathbb{R}}^N$$ . The asymptotic distribution of the eigenvalues is also considered.

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Journal Article

Existence for a degenerate diffusion problem with a nonlinear operator

Favini, Angelo; Marinoschi, Gabriela

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0348-1

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed...

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Journal Article

Perturbations of differentiable semigroups

Iley, Philippa

2007 Journal of Evolution Equations

doi:10.1007/s00028-007-0349-0

If ( A , D ( A )) generates a C 0 -semigroup T on a Banach space X and $$B \in {\mathcal{L}}(X)$$ then ( A + B , D ( A )) is also the generator of a C 0 -semigroup, S B . There are easy examples to show that if T is eventually differentiable then S B need not be eventually differentiable. In 1995...

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Journal of Evolution Equations Volume 7 Issue 4

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