Methods for Partial Differential Equations
Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models
Delivery estimate
Please enter a valid 4-digit Australian postcode.
to ·
Delivery estimate
Please enter a valid 4-digit Australian postcode.
to ·
Methods for Partial Differential Equations
Description
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the "research project for beginners" proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area.
The book is organized in five parts:
In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation.
Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models.
Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results.
Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions.
The last part features selected research projects and general background material.
Shipping & Processing
This item is in stock with our supplier and usually ships within 3–5 business days.
Processing times
- In stock: Items marked “In Stock” are on our shelves. We pick, pack and ship them within 1–2 business days.
- In stock with our supplier: Items not marked “In Stock” are held by one of our Australian or overseas suppliers. We order them in for you and they usually dispatch within 2–5 business days (3–5 for some suppliers). The estimate next to the price is for this item.
- Special orders: Some supplier items, such as specialist and imported items, titles awaiting reprint and print-on-demand titles, take longer to arrive. If your order includes one, we’ll update you as soon as we hear from our supplier.
- Supplier delays: Occasionally a supplier is delayed, or their stock information turns out to be inaccurate. We’ll keep your order open for up to 60 days. If an item hasn’t shipped or isn’t on its way to us by then, we’ll cancel that item and refund it.
How accurate is availability?
Availability is based on the stock levels our suppliers tell us they hold, and we update it regularly. If a supplier issue affects your order, we’ll let you know with an updated estimate.
Delivery
- As soon as your order ships you’ll get an email with tracking.
- Australia Post usually delivers within 2–10 business days of shipping (around 4 in metro areas and around 6 in regional areas).
- If your order has more than one item, we hold the in-stock items until everything is ready, so we can ship your whole order together in one parcel.
- Shipping cost: Free on orders over $100 within Australia, otherwise $9.95 flat rate per order however many items you buy. Free shipping applies to Australian addresses only; delivery to New Zealand is $14.95 per order.
- Check your address: If an order goes to an incorrect address you gave us, or isn’t collected and Australia Post returns it to us, you’ll need to pay the postage to send it again.
Cancellations
Need to change or cancel an order? Contact us as soon as possible at contact@bookloop.com.au or through our contact page.
- Within 30 minutes: You can change or cancel your order for a full refund within 30 minutes of placing it.
- After 30 minutes: Your order is already being processed, so it can no longer be changed or cancelled. If we can accept a late cancellation, we may offer store credit instead of a refund.
- Items in transit: Once an item is on its way, either from our supplier to us or from us to you, it can’t be cancelled. If you no longer want it once it arrives, you can return it as a change of mind, with return postage at your cost. See Returns.
- Separate orders can’t be combined once they’ve been placed, and adding or swapping items can change the delivery estimate.
- Supplier delays: Occasionally a supplier is delayed, or their stock information turns out to be inaccurate. We’ll keep your order open for up to 60 days. If an item hasn’t shipped or isn’t on its way to us by then, we’ll cancel that item and refund it.
Faulty or damaged items are always covered. See Returns.
Returns
Damaged or incorrect items (within 30 days)
If an item arrives damaged or isn’t what you ordered, contact us within 30 days of delivery. We may ask for a photo, and if we need the item back we’ll send a prepaid return label, so it costs you nothing. You’ll receive a replacement or refund, as guaranteed under the Australian Consumer Law.
Change of mind (within 30 days)
We offer a refund or store credit for change of mind within 30 days of purchase when:
- you have your proof of purchase;
- the item is unused and in its original condition and packaging;
- it isn’t a sale item, special order, custom item or gift voucher.
You pay the postage to return change-of-mind items. Change-of-mind returns aren’t available for print-on-demand titles or bulk orders with special pricing.
Returned to sender
If an order is sent to an incorrect address you gave us, or isn’t collected and Australia Post returns it to us, you’ll need to pay the postage to send it again.