The extended tanh method and the exp-function method to solve a kind of nonlinear heat equation.
The Feynman-Kac formula for a system of parabolic equations
The Finite Element Method for Parabolic Equations. I. A Posteriori Error Estimation
The Finite Element Method for Parabolic Equations. II. A Posteriori Error Estimation and Adaptive Approach
The finite element solution of elliptic and parabolic equations using simplicial isoparametric elements
The finite element solution of parabolic equations
In contradistinction to former results, the error bounds introduced in this paper are given for fully discretized approximate soltuions of parabolic equations and for arbitrary curved domains. Simplicial isoparametric elements in -dimensional space are applied. Degrees of accuracy of quadrature formulas are determined so that numerical integration does not worsen the optimal order of convergence in -norm of the method.
The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation
In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.
The finite volume method for an elliptic-parabolic equation.
The first initial-boundary value problem for quasilinear second order parabolic equations
The fourth order accuracy decomposition scheme for an evolution problem
In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.
The fourth order accuracy decomposition scheme for an evolution problem
In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.
The functional calculus for the laplacian on Lipschitz domains
The fundamental solution of a modified Oseen problem.
The fundamental solutions for fractional evolution equations of parabolic type.
The fundamental solutions for fractional evolution equations of parabolic type.
The generalized Burgers equation with and without a time delay.
The generalized Conley index and multiple solutions of semilinear elliptic problems.
The genuinely nonlinear Graetz-Nusselt ultraparabolic equation.
The Geometry of Differential Harnack Estimates
In this short note, we hope to give a rapid induction for non-experts into the world of Differential Harnack inequalities, which have been so influential in geometric analysis and probability theory over the past few decades. At the coarsest level, these are often mysterious-looking inequalities that hold for ‘positive’ solutions of some parabolic PDE, and can be verified quickly by grinding out a computation and applying a maximum principle. In this note we emphasise the geometry behind the Harnack...
The version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems.