A priori bounds for solutions of parabolic problems and applications
We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.
A priori bounds for solutions of parabolic problems and applications
A priori error estimates for reduced order models in finance
Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error...
A priori estimates for global solutions and multiple equilibria of a superlinear parabolic problem involving measures.
A priori estimates in weighted spaces for solutions of the Poisson and heat equations
We prove a priori estimates for solutions of the Poisson and heat equations in weighted spaces of Kondrat'ev type. The weight is a power of the distance from a distinguished axis.
A priori estimates of solutions of superlinear problems
In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.
A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation.
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
A problem of thermal shock with thermal relaxation.
A problem with internal conditions for a pseudoparabolic equation.
A problem with nonlocal boundary conditions for a quasilinear parabolic equation.
A qualitative study on a parabolic free boundary problem.
A qualitative theory for parabolic problems under dynamical boundary conditions.
A quasi-linear parabolic system of chemotaxis.
A quasilinear parabolic system with nonlocal boundary condition.
A quasi-variational inequality problem arising in the modeling of growing sandpiles
Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...
A reaction-diffusion equation on a net-shaped thin domain
A Reduced Model for Flame-Flow Interaction
The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system of second-order...
A regularity theorem for curvature flows.
A remark on a Harnack inequality for degenerate parabolic equations