Abstract We study a first-order nonlinear partial differential equation and present necessary sufficient condition for the global existence of its solution in non-smooth environment. Using this result, we prove local theorem to equation. Moreover, two applications result. The first concerns an inverse problem called integrability microeconomic theory second extension Frobenius’ theorem.

This article describes a novel nonlinear second-order PDE model for image filtering. The proposed denoising model is based on a second-order hyperbolic equation and provides effective detail-preserving image noise removal results. The well-posedness of this nonlinear PDE scheme is then investigated in this paper. A finite-difference based explicit numerical approximation scheme is constructed n...

This note is devoted to stabilizing a coupled PDE–ODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE–ODE cascadewith an invertible integral transformation,where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, a...

A detailed model of the memory performance of a PDE solver running on a NUMA-system is set up. Due to the complexity of modern computers, such a detailed model inevitably is very complicated. Therefore, approximations are introduced that simplify the model and allows NUMA-systems and PDE solvers to be described conveniently. Using the simpli ed model, it is shown that PDE solvers using ordered ...

In this paper, we study a partial differential equation (PDE) framework for option pricing where the underlying factors exhibit stochastic correlation, with an emphasis on computation. We derive a multi-dimensional time-dependent PDE for the corresponding pricing problem, and present a numerical PDE solution. We prove a stability result, and study numerical issues regarding the boundary conditi...

A new fast likelihood computation approach is proposed for HMM-based continuous speech recognition. This approach is an extension of the partial distance elimination (PDE) technique. Like PDE, the extended PDE (EPDE) approach aims at finding the most prominent Gaussian in a GMM for a given observation, and approximating the GMM’s likelihood with the identified Gaussian. EPDE relies on a novel s...

For scalar time-dependent variable-coefficient PDE, it has been demonstrated that Krylov subspace spectral (KSS) methods achieve high-order accuracy and also possess highly desirable stability properties, especially considering that they are explicit. In this paper, we examine the generalization of these methods to systems of variable-coefficient PDE by selection of appropriate bases of trial a...