Applied Mathematics and Optimization

Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not applicable in this scenario, and additional assumptions are ...

We show how the sticky dynamics for the one-dimensional pressureless Euler-alignment system can be obtained as an $L^2$-gradient flow of a convex functional. This is analogous to the Lagrangian evolution introduced by Natile and Savaré for the ...

This paper investigates a linear-quadratic (LQ) Stackelberg game for mean-field type backward stochastic system, in which the cost functional is also mean-field type. In our model, the leader first announces the terminal goal satisfying pointwise ...

We study a system described by a type of initial and boundary value problem of the Hirota equation with nonhomogeneous boundary conditions posed on a bounded interval. Firstly, we prove the local well-posedness of the system in the space $H^s(0,1)$ ...$\mathrm{}$${}^{\mathrm{}}\mathrm{}\mathrm{}$${}^{\mathrm{}}\mathrm{}\mathrm{}$${}^{\mathrm{}}\mathrm{}\mathrm{}$${}^{\mathrm{}}\mathrm{}\mathrm{}$

The Earth’s climate system naturally adjusts to maintain a balance between the energy received from the Sun and the energy reflected back into space, a concept known as the “Earth’s radiation budget”. However, this balance has been disrupted by ...

Loosely speaking, the Navier–Stokes-$\alpha$ model and the Navier–Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier–Stokes-$\alpha$ model driven by a multiplicative ...$\mathrm{}$

We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton–Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with respect ...

We prove the null controllability of forward and backward linear stochastic parabolic equations with first and zero order coupling terms, and with bounded coefficients. The null controllability results rely on novel Carleman estimates for the ...

This paper discusses an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy ...$\mathrm{}{\mathbb{}}^{}\mathrm{}\mathrm{}$$\mathrm{}\mathrm{}\mathrm{}$$\mathrm{}$$\mathrm{}$