Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction [PDF]
, 2004 A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions.
Abraham +16 more
core +2 more sources
Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
International Journal of Mathematics and Mathematical Sciences, 1989 The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques.
G. Adomian
doaj +1 more source
A new method for exact product form and approximation solutions of a parabolic equation with nonlocal initial condition using Ritz method [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2020 Many phenomena in various fields of physics are simulated by parabolic partial differential equations with the nonlocal initial conditions, while there are few numerical methods for solving these problems.
Z. Barikbin
doaj +1 more source
Optimality Conditions for Semilinear Parabolic Equations with Controls in Leading Term [PDF]
, 2010 An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation.
Lou, Hongwei
core +2 more sources
Modeling Heavy Metal Sorption and Interaction in a Multispecies Biofilm
Mathematics, 2019 A mathematical model able to simulate the physical, chemical and biological interactions prevailing in multispecies biofilms in the presence of a toxic heavy metal is presented.
Berardino D’Acunto +3 more
doaj +1 more source
Existence results for a fourth order partial differential equation arising in condensed matter physics [PDF]
, 2015 We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We consider this
Escudero, Carlos +4 more
core +2 more sources
Resonance and Quasilinear Parabolic Partial Differential Equations
Journal of Differential Equations, 1993 For a certain quasilinear parabolic equation, the authors prove the existence of a weak periodic solution in an adequate Hilbert space under both resonance and nonresonance conditions. The results are obtained by using a Galerkin-type technique.
Lefton, L.E., Shapiro, V.L.
openaire +2 more sources
مجلة بغداد للعلوم, 2010 The aim of this paper is to approximate the solution of the parabolic partial differential equations (heat equations) using Bellman's method with the cooperation of the G-spline interpolation formula.
Osama H. Mohammed
doaj +1 more source
Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations [PDF]
, 2014 Based on a recent result on linking stochastic differential equations on ℝ d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path ...
A Majda +39 more
core +1 more source
Analytical expansions for parabolic equations [PDF]
, 2014 We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short ...
Lorig, Matthew +2 more
core +3 more sources