«source term»
۷۸٬۵۲۱ نتیجهOn the blow up of solutions for hyperbolic equation involving the fractional Laplacian with source terms
In this paper, we study the blow-up of solutions for hyperbolic equations involving the fractional Laplacian operator with damping and source terms. We obtain the global existence results. Then, we observe the blow-up of solutions using the concavity method. Finally, we present s
The geometric properties of a degenerate parabolic equation with periodic source term
In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface
Singularly perturbed robin type boundary value problems with discontinuous source term in geophysical fluid dynamics
Singularly perturbed robin type boundary value problems with discontinuous source terms applicable in geophysical fluid are considered. Due to the discontinuity, interior layers appear in the solution. To fit the interior and boundary layers, a fitted nonstandard numerical method
the geometric properties of a degenerate parabolic equation with periodic source term
in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface
Robust numerical approach for singularly perturbed parabolic problems with discontinuous convection coefficients and source terms
This study explores the numerical method for 1 − D singularly perturbed parabolic problems, influenced by two distinct parameters affecting diffusion and convection. With discontinuous convection and source terms, the solutions exhibit boundary and interior layers due to the pert
Blow-up phenomena for a couple of parabolic equations with memory and source terms: Analytical and simulation
In this paper, the focus is on investigating the asymptotic behavior of the solution for a system of parabolic equations with memory terms acting in both equations. This system has many applications in various scientific fields, including heat conduction in materials with memory
A Sensitivity and Adjoint Calculus for Discontinuous Solutions of Hyperbolic Conservation Laws with Source Terms
We present a sensitivity and adjoint calculus for the control of entropy solutions of scalar conservation laws with controlled initial data and source term. The sensitivity analysis is based on shift-variations which are the sum of a standard variation and suitable corrections by
Analysis of Dual Consistency for Discontinuous Galerkin Discretizations of Source Terms
The effects of dual consistency on discontinuous Galerkin (DG) discretizations of solution and solution gradient dependent source terms are examined. Two common discretizations are analyzed: the standard weighting technique for source terms and the mixed formulation. It is shown
A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms
The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, lead
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term
and Applied Analysis 3 Baeumer et al. 8, 13 have proved existence and uniqueness of a strong solution for 1.2 using the semigroup theory when f x, t, u is globally Lipschitz continuous. Furthermore, when f x, t, u is locally Lipschitz continuous, existence of a unique strong solu