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Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations
MathematicsThe optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic ...
Yang Na +3 more
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Uniqueness of Entropy Solutions of Nonlinear Elliptic-Parabolic-Hyperbolic Problems in One Dimension Space [PDF]
, 2009 We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form b(u)t — a(u, φ(ux)x= f with homogeneous Dirichlet conditions and initial conditions.
Ouaro, Stanislas
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$L^1$ contraction for bounded (non-integrable) solutions of degenerate parabolic equations [PDF]
, 2014 We obtain new $L^1$ contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or non-local diffusion terms.
Endal, J., Jakobsen, E. R.
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Difference schemes for degenerate parabolic equations [PDF]
Mathematics of Computation, 1986 Diagonal dominant implicit-difference schemes approximating a porous media type class of multidimensional nonlinear equations are shown to generate semigroups in an approximate L 1 {L^1} -space, and the rate of convergence to the semigroup solution in L 1
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Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions
Abstract and Applied Analysis, 2006 We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots.
Adelaida B. Vasil'eva +1 more
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, 2015 We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001).
Ley, Olivier, Nguyen, Vinh Duc
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Riesz potentials and nonlinear parabolic equations [PDF]
, 2013 The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation.
A. Cianchi +31 more
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Impulsive Quenching for Degenerate Parabolic Equations
Journal of Mathematical Analysis and Applications, 1996 An impulsive problem for a singular degenerate parabolic equation is studied. Sufficient conditions for the existence of a unique critical length are given. The critical length \(a^*\) is the length of the space interval such that the solution with zero initial and boundary data quenches for intervals larger than \(a^*\) but it exists globally for ...
Chan, C.Y., Kong, P.C.
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Null controllability of degenerate parabolic operators with drift
Networks and Heterogeneous Media, 2007 We give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain.
Piermarco Cannarsa +2 more
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The cost of controlling strongly degenerate parabolic equations [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2020 We consider the typical one-dimensional strongly degenerate parabolic operator Pu = ut − (xαux)x with 0 < x < ℓ and α ∈ (0, 2), controlled either by a boundary control acting at x = ℓ, or by a locally distributed control. Our main goal is to study the dependence of the so-called controllability cost needed to drive an initial condition to rest ...
Cannarsa, P. +2 more
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