where Ω ⊂ R and Γ is the boundary of Ω. In this case μΩ is a bounded Radon measure on Ω× J and μΓ is such a measure on Γ× J . In [10] the semilinear analogues of (0.1) and (0.2), where μ and (μΩ, μΓ), respectively, may also depend nonlinearly and nonlocally on the unknown solution u, are investigated. Based on the results of [5], general existence, uniqueness, and continuity theorems are proved...

We study retarded parabolic non{autonomous evolution equations whose coeecients converge as t ! 1 such that the autonomous problem in the limit has an exponential dichotomy. Then the non{autonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation tends to the stationary solution at innnity. We use a generalized characteristic equation to deduce the expon...

We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583-2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending on...

It is shown that a function u satisfying |∂t + u| M (|u| + |∇u|), |u(x, t)| MeM|x| in (R \ BR) × [0, T ] and u(x, 0) = 0 for x ∈ R \ BR must vanish identically in R \ BR × [0, T ].

In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximumnorm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L∞(QT ) and L p((0, T ); Lq ( )), 1 < p, q < ∞....

the kinetics of zn sorption by ten calcareous soils of iran were measured and fitted to several equations (zero-, first-, second-, third-order, parabolic diffusion, simple elovich, and exponential equations). two initial concentrations of zinc i.e. 20 and 80 mg zn l-1 were used and observations were carried out for 100 hours. the time required to reach the near equilibrium state was about 24 ho...

We consider global bounded solutions of fully nonlinear parabolic equations on bounded reflectionally symmetric domains, under nonhomogeneous Dirichlet boundary condition. We assume that, as t→∞, the equation is asymptotically symmetric, the boundary condition is asymptotically homogeneous, and the solution is asymptotically strictly positive in the sense that all its limit profiles are strictl...

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...