Results 21 to 30 of about 39,676 (281)

Second order mean field games with degenerate diffusion and local coupling [PDF]

, 2014
We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility ...
Cardaliaguet, Pierre, Graber, J., Porretta, Alessio, Tonon, Daniela   +3 more
core   +5 more sources

Convergence for Degenerate Parabolic Equations

Journal of Differential Equations, 1999
The authors consider degenerate parabolic problems of the form \[ \begin{aligned} u_t-\varphi \bigl(u(x,t) \bigr)_{xx}= f\bigl(u(x,t) \bigr),\quad & x\in (-L,L),\;t>0,\\ u(-L,t)= u(L,t)=0, \quad & t>0,\\ u(x,0)= u_0(t)\geq 0,\quad & x\in (-L,L), \end{aligned} \] where \(\varphi\) and \(f\) are sufficiently regular functions satisfying \(\varphi(0)=0\),
Feireisl, Eduard, Simondon, Frédérique
openaire   +2 more sources

Null controllability of degenerate parabolic equation with memory [PDF]

Mathematical Methods in the Applied Sciences, 2021
In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat equation via new Carleman estimates with weighted time functions that do not blow up at .
Allal, Brahim, Fragnelli, Genni
openaire   +5 more sources

Interior degenerate/singular parabolic equations in nondivergence form: well-posedness and Carleman estimates [PDF]

, 2015
We consider non smooth general degenerate/singular parabolic equations in non divergence form with degeneracy and singularity occurring in the interior of the spatial domain, in presence of Dirichlet or Neumann boundary conditions.
Alabau-Boussouira, Arendt, Baras, Baras, Beauchard, Boutaayamou, Boutaayamou, Brezis, Brezis, Cannarsa, Cannarsa, Cannarsa, Cannarsa, Cazenave, de Castro, Dold, Ervedoza, Floridia, Fotouhi, Fotouhi, Fragnelli, Fragnelli, Fragnelli, Fragnelli, Fragnelli, Galaktionov, Genni Fragnelli, Le Rousseau, Taylor, Vancostenoble, Vancostenoble   +30 more
core   +2 more sources

Stability for degenerate parabolic equations [PDF]

Advances in Calculus of Variations, 2010
The authors study the stability of the solutions of the evolutionary \(p\)-Laplace equation \[ {\partial u\over\partial t}= \nabla\cdot(|\nabla u|^{p-2}\nabla u) \] under variations of the parameter \(p\). The problem is delicate, since the underlying Sobolev space varieties with \(p\). The boundary values are given on the parabolic boundary of a space-
Parviainen, Mikko, Kinnunen, Juha
openaire   +4 more sources

Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states

, 2020
In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence form governed ...
Floridia, Giuseppe, Nitsch, Carlo, Trombetti, Cristina   +2 more
core   +1 more source

Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications [PDF]

, 2006
In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations.
Alvarez Olivier, Barles G., Bensoussan Alain, Benth Fred, Crandall Michael, Evans Lawrence, Fleming Wendell, Francesca Da Lio, John Fritz, Ley Olivier, Olivier Ley   +10 more
core   +8 more sources

Expansion of positivity to a class of doubly nonlinear parabolic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2022
We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering ...
Eurica Henriques
doaj   +1 more source

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, Leonid V. Kalachev   +1 more
doaj   +2 more sources

Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

Mathematics
The 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, Tianjiao Men, Runmei Du, Yingjie Zhu   +3 more
doaj   +1 more source