Variations of heat equation on the half‐line via the Fokas method
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DOI: 10.1002/mma.10303
Abstract: In this review paper, we discuss some of our recent results concerning the rigorous analysis of initial boundary value problems (IBVPs) and newly discovered effects for certain evolution partial differential equations (PDEs). These equations arise… read more here.
Keywords: method; variations heat; fokas; equation half ... See more keywords
Initial Boundary Value Problem for Partial Differential–Algebraic Equations With Parameter
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DOI: 10.1002/mma.10663
Abstract: The paper addresses an initial boundary value problem for a partial differential–algebraic equation involving a parameter. An integral condition with respect to the time derivative of the unknown function is provided as an additional condition… read more here.
Keywords: problem; boundary value; value problem; initial boundary ... See more keywords
Integral Representation of Solutions to Initial‐Boundary Value Problems on a Finite Interval in the Framework of the Hyperbolic Heat Equation
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DOI: 10.1002/mma.11140
Abstract: We consider initial‐boundary value problems on a finite interval for the system of the energy balance equation and modified Fourier's law (constitutive equation, commonly called the Cattaneo equation) describing temperature (or internal energy) and heat… read more here.
Keywords: equation; heat; value problems; boundary value ... See more keywords
Global existence of solutions of initial boundary value problem for nonlocal parabolic equation with nonlocal boundary condition
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DOI: 10.1002/mma.6286
Abstract: We prove the global existence and blow‐up of solutions of an initial boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for… read more here.
Keywords: boundary value; global existence; nonlocal parabolic; solutions initial ... See more keywords
Modeling of uncertainty for flood wave propagation induced by variations in initial and boundary conditions using expectation operator on explicit numerical solutions
Sign Up to like & getrecommendations! Published in 2018 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.5702
Abstract: This study proposes a framework for uncertainty analysis by incorporating explicit numerical solutions of governing equations for flood wave propagation with the expectation operator. It aims at effectively evaluating the effect of variations in initial… read more here.
Keywords: explicit numerical; uncertainty; initial boundary; numerical solutions ... See more keywords
GENERIC-based formulation and discretization of initial boundary value problems for finite strain thermoelasticity
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DOI: 10.1007/s00466-019-01781-5
Abstract: A new variational formulation for finite strain thermoelastodynamics is proposed. The variational formulation emanates from the GENERIC formalism and makes possible the free choice of the thermodynamic state variable. In particular, one may choose the… read more here.
Keywords: finite strain; state variable; initial boundary; formulation ... See more keywords
How to avoid order reduction when Lawson methods integrate nonlinear initial boundary value problems
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DOI: 10.1007/s10543-021-00879-8
Abstract: It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space or do not satisfy enough conditions of annihilation… read more here.
Keywords: initial boundary; order; order reduction; lawson methods ... See more keywords
Modeling of the Processes of Heterodiffusion in Two Ways for the Cascade Decay of Admixture Particles. І. Cascade-Type Initial-Boundary-Value Problems
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DOI: 10.1007/s10958-021-05294-6
Abstract: We study the processes of heterodiffusion of admixtures in the case of their cascade decay in a body with two ways of migration accompanied by the mass exchange between states. For the case of unbranched… read more here.
Keywords: cascade type; cascade decay; initial boundary; processes heterodiffusion ... See more keywords
Reproducing Kernel Method for Singularly Perturbed One-Dimensional Initial-Boundary Value Problems with Exponential Initial Layers
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DOI: 10.1007/s12346-017-0242-3
Abstract: In this paper, a meshless numerical method is proposed for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers. The method is a combination of the domain decomposition method and the reproducing kernel method.… read more here.
Keywords: singularly perturbed; reproducing kernel; initial boundary; one dimensional ... See more keywords
Boundary value technique based on a fifth derivative method of order 10 for fourth order initial and boundary value problems
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DOI: 10.1007/s13370-018-0572-6
Abstract: In this paper, the fourth order ordinary differential equation (ODE) of the form $$y^{(iv)}=f(x,y,y',y'',y''')$$y(iv)=f(x,y,y′,y′′,y′′′) subject to initial or boundary conditions is solved directly without reducing the higher ODE into an equivalent first order system. This… read more here.
Keywords: order; initial boundary; method; fifth derivative ... See more keywords
On the initial-boundary value problem for some quasilinear parabolic equations of divergence form
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DOI: 10.1016/j.jde.2017.08.056
Abstract: Abstract In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form u t − div { σ ( |… read more here.
Keywords: initial boundary; quasilinear parabolic; value problem; boundary value ... See more keywords