1,720,974 research outputs found
Correction to: Two generalized Tricomi equations (Calculus of Variations and Partial Differential Equations, (2021), 60, 3, (84), 10.1007/s00526-021-01970-2)
No full textA correction to this paper has been published: https://doi.org/10.1007/s00526-021-02024-3
Further existence results for elliptic–parabolic and forward–backward parabolic equations
Full text linkWe give an existence result for first order evolution equation of the type Ru′+ Au= f where R may be a function depending also on time assuming positive, null and negative sign, then the equation may be elliptic–parabolic, both forward and backward. The result is given in an abstract setting with Banach spaces depending on time (the functions u are defined in an interval [0, T] and u(t) ∈ X(t) for a.e. t) and R which is in fact a linear operator. We also extend a previous existence result for the equation (Ru) ′+ Au= f to the setting of moving Banach spaces. We also give a time regularity result in a particular case and give many examples of different possible choices of R
An Apparently Unnatural Estimate About Forward-Backward Parabolic Equations
Full text linkIn this note we come back to face a problem regarding forward-backward parabolic equations like(Formula Presented)both positive and negative): the continuity o
Boundedness for solutions of weighted forward–backward parabolic equations without assuming higher regularity
No full textWe consider the solutions of two evolution equations of the type μ(x,t)ut+Au=0 and (μ(x,t)u)t+Au=0, where μ∈L1 may be positive, null and negative and A a suitable monotone operator. The simple example is A=−Δp with p⩾2. For these functions we prove an unusual local boundedness result using an approximation via the solutions of suitable equations, specifically ɛBu+μ(x,t)ut+Au=0 and ɛBu+(μ(x,t)u)t+Au=0. For A=−Δp, Bu=−(|ut|p−2ut)t
Elliptic approximation of forward-backward parabolic equations
Full text linkIn this note we give existence and uniqueness result for some elliptic problems depending on a small parameter and show that their solutions converge, when this parameter goes to zero, to the solution of a mixed type equation, elliptic-parabolic, parabolic both forward and backward. The aim is to give an approximation result via elliptic equations of a changing type equation
Two generalized Tricomi equations
Full text linkIn this note we give existence results for the generalized Tricomi equations Ru′ ′+ Bu= f and (Ru′)′+Bu=f with suitable boundary data where R may be an operator (or a function) depending also on time assuming positive, null and negative sign, while B is an elliptic operator. To do that we also extend a result for equations like (Ru′)′+Au′+Bu=f to equations like Ru′ ′+ Au′+ Bu= f and use these to derive the existence for the generalised Tricomi type equations mentioned above
LOCAL BOUNDEDNESS FOR FORWARD-BACKWARD PARABOLIC DE GIORGI CLASSES WITHOUT ASSUMING HIGHER REGULARITY
No full textWe define a homogeneous De Giorgi class of order p >= 2 that contains the solutions of two evolution equations of elliptic-parabolic and forward-backward parabolic type like p(x, t)u(t)+ Au = 0 and (p(x, t)u)(t)+ Au = 0, where p, for simplicity, takes values in the set {-1, 0, 1}, and A a suitable monotone operator. For functions belonging to this class, we prove an unusual local boundedness result
G-convergence of elliptic and parabolic operators depending on vector fields
Full text linkWe consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence, or H-convergence, by means of the compensated compactness theory, in a setting in which the existence of affine functions is not always guaranteed, due to the nature of the family of vector fields
Effective anisotropy tensor for the numerical solution of flow problems in heterogeneous porous media
No full textThe numerical solution of porous media flow equations often requires the computationof discrete interfacial average fluxes. Standard methods, such as Integrated Finite Differences(IFD) or Finite Volumes (FV), rely on the definition of average gradients of thesolution, and calculate the interface fluxes by means of appropriate averages of the conductivitytensor K. The question of how to choose a correct average for the conductivityin the anisotropic case is however still open. We derive a procedure based on conservationof flux and energy, which is particularly suited for non-asymptotical regimes, at afixed mesh (size). The resulting effective tensor provides standard arithmetic-harmonicmeans of tensor coefficients with respect to tangential and normal components of thegradient in simple cases. Moreover, this tensor is shown to coincide with a matrix arisingfrom homogenization theory, even though it has been obtained for different purposes,and following a different approach. The effectiveness of the proposed method is verifiednumerically.http://proceedings.cmwr-xvi.or
- …
