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This volume is the result of lectures delivered at the second meeting on the subject of nonlinear partial differential equations, held at Tohoku University, 27-29 February 1984. The topics presented at the conference range over various fields of mathematical physics.

Differential equations, Partial --- Differential equations, Nonlinear

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Partial differential equations --- Differential equations, Partial --- Differential equations, Partial. --- Équations aux dérivées partielles

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Boundary value problems. --- Differential equations, Partial. --- Discontinuous functions. --- Function spaces.

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Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

Banach spaces --- Differential equations, Linear --- Differential equations, Partial

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Partial differential equations --- Differential equations, Partial. --- Level set methods. --- Maximum principles (Mathematics) --- Maximum principles (Mathematics).