Solution spectrum of nonlinear diffusion equations

Journal Article · Sat Aug 01 04:00:00 EDT 1992 · International Journal of Theoretical Physics

DOI:https://doi.org/10.1007/BF00673985· OSTI ID:136162

Ulmer, W ^[1]

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1. FB Radiotherapy, Department Medizinphysik/Biophysik, Klinikum Amberg (Germany)

The stationary version of the nonlinear diffusion equation -{partial_derivative}c/{partial_derivative}t+D{Delta}c=A{sub 1}c-A{sub 2}c{sup 2} can be solved with the ansatz c={summation}{sub p=1}{sup {infinity}} A{sub p}(cosh kx){sup -p}, inducing a band structure with regard to the ratio {lambda}{sub 1}/{lambda}{sub 2}. The resulting solution manifold can be related to an equilibrium of fluxes of nonequilibrium thermodynamics. The modification of this ansatz yielding the expansion c={summation}{sub p,q=1}{sup infinity}A{sub pa}(cosh kx){sup -p}[(cosh {alpha}t){sup -q-1} sinh {alpha}t+b(cosh {alpha}t){sup -q}] represents a solution spectrum of the time-dependent nonlinear equations, and the stationary version can be found from the asymptotic behaviour of the expansion. The solutions can be associated with reactive processes such as active transport phenomena and control circuit problems is discussed. There are also applications to cellular kinetics of clonogenic cell assays and spheriods. 33 refs., 1 tab.

• Sponsoring Organization: USDOE
• OSTI ID: 136162
• Journal Information: International Journal of Theoretical Physics, Journal Name: International Journal of Theoretical Physics Journal Issue: 8 Vol. 31; ISSN 0020-7748; ISSN IJTPBM
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANALYTICAL SOLUTION
DIFFUSION
FOKKER-PLANCK EQUATION
KINETIC EQUATIONS
NONLINEAR PROBLEMS
THERMODYNAMICS